Henri Darmon - Publications

If you have access to MathSciNet, you can read the reviews of my papers in Math Reviews.

Research Articles and Monographs

85. pdf.

Lea Beneish, Henri Darmon, Lennart Gehrmann and Marti Roset.
The Gross-Kohnen-Zagier theorem via p-adic uniformization.
submitted.

84. pdf.

Henri Darmon and Alice Pozzi.
Flach classes and generalised Hecke eigenvalues.
submitted.

83. pdf.

Henri Darmon and Michele Fornea.
Mock plectic points.
submitted.

82. pdf.

Henri Darmon and Jan Vonk.
p-adic Green's functions for real quadratic geodesics.
submitted.

81. pdf.

Henri Darmon, Alan Lauder, and Victor Rotger.
Elliptic Stark conjectures and exceptional weight one forms
Submitted.

80. pdf, lecture at KIAS.

Henri Darmon, Lennart Gehrmann, and Mike Lipnowski.
Rigid meromorphic cocycles for orthogonal groups.
Submitted.

79. pdf, published version, lecture at IHES by Akshay Venkatesh.

Henri Darmon, Michael Harris, Victor Rotger, and Akshay Venkatesh.
The derived Hecke algebra for dihedral weight one forms.
Michigan Mathematics Journal 72, 145-207 (2022).

78. pdf.

Sofia Giampietro and Henri Darmon.
A p-adic approach to singular moduli on Shimura curves.
Involve, 15 (2022) pp. 345-365.`

77. pdf, published version.

Massimo Bertolini, Henri Darmon, and Rodolfo Venerucci.
Heegner points and Beilinson-Kato elements: a conjecture of Perrin-Riou.
Advances in Math, 398 108172 pp. 1-50 (2022).

76. pdf, lecture in Regensburg by Alice Pozzi.

Henri Darmon, Alice Pozzi and Jan Vonk.
The values of the Dedekind-Rademacher cocycle at real multiplication points
Journal of the European Mathematical Society, to appear.

75. pdf, published version.

Henri Darmon and Jan Vonk.
Arithmetic intersections of modular geodesics.
Journal of Number Theory (2021). Proceedings of the first JNT biennial conference in Cetraro.

74. pdf. published version.

Henri Darmon and Alan Lauder.
Stark points on elliptic curves via Perrin-Riou's philosophy
Annales Mathematiques du Quebec (2021). (Special birthday issue for Bernadette Perrin-Riou.)

73. pdf, published version.

Henri Darmon, Alice Pozzi and Jan Vonk.
Diagonal restrictions of p-adic Eisenstein families
Mathematische Annalen 379 503--548 (2021)

72. pdf, published version.

Henri Darmon and Jan Vonk.
Real quadratic Borcherds products.
Pure and Applied Mathematics Quarterly (special issue in honor of Dick Gross), Volume 18, Number 5, 1803-1865, (2022)

The material in this paper extends and largely supersedes the unpublished article
Ring class fields of real quadratic fields and cuspidal values of rigid meromorphic cocycles
pdf.

71. pdf.

Henri Darmon.
The p-adic uniformisation of modular curves by p-arithmetic groups
Proceedings of a conference marking the 80th Birthday of Yasutaka Ihara, RIMS, Kyoto.

70. pdf.

Henri Darmon and Victor Rotger.
Stark-Heegner points and diagonal classes
and
p-adic families of diagonal cycles.
in Astérisque 434, Heegner points, Stark-Heegner points, and Diagonal Classes, (2022).

The material in these two papers largely subsumes the unpublished preprint
Stark-Heegner points and generalised Kato classes pdf.

69. pdf, published version.

Henri Darmon and Jan Vonk.
Singular moduli for real quadratic fields: a rigid analytic approach.
Duke Math Journal, 170, Number 1 (2021), 23-93.

Lecture by Jan Vonk at the IAS
Lecture by Henri Darmon at the IAS

68. pdf.

Henri Darmon, Alan Lauder and Victor Rotger
First order p-adic deformations of weight one newforms.
"Heidelberg conference on L-functions and automorphic forms", Contrib.Math.Comput.Sci. 10, Springer, (2017) 39-80.

67. pdf, published Version.

Henri Darmon and Victor Rotger
Elliptic curves of rank two and generalised Kato classes.
Research in Mathematics, Special issue in memory of Robert Coleman, 3:27 (2016).

66. pdf, published version.

Henri Darmon, Alan Lauder and Victor Rotger
Overconvergent generalised eigenforms of weight one and class fields of real quadratic fields.
Advances in Mathematics 283 (2015) 130-142.

65. pdf, published version.

Henri Darmon, Alan Lauder and Victor Rotger
Gross-Stark units and p-adic iterated integrals attached to modular forms of weight one.
Annales des Sciences Mathématiques du Québec, Special issue marking the 60th birthday of Glenn Stevens, 40 (2016) 325-354.

64. pdf, published version.
Slightly revised version, with minor corrections written in blue.

Henri Darmon, Alan Lauder and Victor Rotger
Stark points and p-adic iterated integrals attached to modular forms of weight one.
Forum of Mathematics, Pi (2015), Vol. 3, e8, 95 pages.

63. pdf, published version.

Henri Darmon and Victor Rotger.
Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-series.
Journal of the AMS, 30, Vol. 3, (2017) 601-672.

62. pdf. published version.

Henri Darmon and Victor Rotger
Diagonal cycles and Euler systems I: A p-adic Gross-Zagier formula.
Annales Scientifiques de l'Ecole Normale Supérieure, 47 no. 4 (2014) 779-832.

61. pdf.

Massimo Bertolini, Francesc Castella, Henri Darmon, Samit Dasgupta, Kartik Prasanna, and Victor Rotger.
p-adic L-functions and Euler systems: a tale in two trilogies.
in Automorphic forms and Galois representations, London Mathematical Society Lecture Notes Series 414, (2014), pp 52-101.

60. pdf, published version.

Massimo Bertolini and Henri Darmon
Kato's Euler system and rational points on elliptic curves I: A p-adic Beilinson formula.
Israel Journal of Mathematics, 199, Issue 1, January 2014, 163-188.

59. pdf, published version.

Massimo Bertolini, Henri Darmon and Victor Rotger
Beilinson-Flach elements and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-series.
Journal of Algebraic Geometry 24 (2015) 569-604.

58. pdf, published version.

Massimo Bertolini, Henri Darmon and Victor Rotger
Beilinson-Flach elements and Euler systems I: syntomic regulators and p-adic Rankin L-series.
Journal of Algebraic Geometry 24 (2015), 355-378.

57. pdf, published version.

Massimo Bertolini, Henri Darmon and Kartik Prasanna.
p-adic L-functions and the coniveau filtration on Chow groups.
Journal fur die Reine und Angewandte Mathematik 731 (2017) 21-86.

56. pdf, published version.

Henri Darmon, Michael Daub, Sam Lichtenstein, and Victor Rotger
(With an appendix by William Stein)
Algorithms for Chow-Heegner points via iterated integrals.
Mathematics of Computation 84 (2015) 2505-2547.

55. pdf, published version.

Henri Darmon, Victor Rotger, and Ignacio Sols
Iterated integrals, diagonal cycles, and rational points on elliptic curves.
Publications Mathématiques de Besançon, vol.2, 2012, pp. 19-46.

54. pdf, published Version, errata.

Massimo Bertolini, Henri Darmon, David Lilienfeldt, and Kartik Prasanna
Generalised Heegner cycles and the complex Abel-Jacobi map.
Mathematische Zeitschrift (2020).

53. pdf, published version.

Massimo Bertolini, Henri Darmon, and Kartik Prasanna
Chow-Heegner points on CM elliptic curves and values of p-adic L-functions.
Int. Math. Res. Notices (2014) Vol. 2014, 745-793.

52. pdf. published version.

Massimo Bertolini, Henri Darmon, and Kartik Prasanna
p-adic Rankin L-series and rational points on CM elliptic curves
Pacific Journal of Mathematics, Vol. 260, No. 2, 2012. pp. 261-303.

51. pdf, published version.

Massimo Bertolini, Henri Darmon, and Kartik Prasanna
Generalised Heegner cycles and p-adic Rankin L-series.
Duke Math Journal, Vol. 162, No. 6, (2013) pp. 1033-1148.

50. pdf.

Henri Darmon, Victor Rotger and Yu Zhao
The Birch and Swinnerton-Dyer conjecture for Q-curves and Oda's period relations.
``Geometry and Analysis of Automorphic forms of several variables", Proceedings of the International Symposium in Honor of Takayuki Oda on the Occasion of his 60th birthday, Series on Number Theory and its applications, Vol. 7, Yoshinori Hamahata, Takashi Ichikawa, Atsushi Murase, and Takashi Sugano, eds., World Scientific, 2012, pp. 1-40.

49. pdf, published version.

Samit Dasgupta, Henri Darmon, and Robert Pollack
Hilbert modular forms and the Gross-Stark conjecture
Annals of Math. (2) 174 (2011), no. 1, 439-484.

48. pdf, final version.

Henri Darmon and Gonzalo Tornaria
Stark-Heegner points and the Shimura correspondence
Compositio Mathematica, 144 (2008) 1155-1175.

47. pdf, published version.

Henri Darmon and Ye Tian.
Heegner points over towers of Kummer extensions
Canadian Journal of Mathematics, 62, No. 5 (2010) 1060-1082.

46. pdf, published version.

Pierre Charollois and Henri Darmon
Arguments des unités de Stark et périodes de séries d'Eisenstein
Algebra Number Theory 2 (2008), no. 6, 655-688.

45. pdf

Henri Darmon
Heegner points, Stark-Heegner points, and values of L-series
International Congress of Mathematicians. Vol. II, 313-345, Eur. Math. Soc., Zurich, 2006.

44. pdf

Massimo Bertolini, Henri Darmon and Samit Dasgupta
Stark-Heegner points and special values of L-series
L-Functions and Galois Representations. London Mathematical Society Lecture Note Series 320, (2007) p. 1-23, D. Burns, K. Buzzard, and J. Nekovar, eds.

43. pdf, published version.

Massimo Bertolini and Henri Darmon
The rationality of Stark-Heegner points over genus fields of real quadratic fields
Annals of Mathematics, 170 (2009) 343-369.

42. pdf, published version.

Massimo Bertolini and Henri Darmon
Hida families and rational points on elliptic curves
Inventiones Mathematicae 168 (2007), no. 2, 371-431.

41. pdf

Massimo Bertolini, Henri Darmon and Adrian Iovita
Families of automorphic forms on definite quaternion algebras and Teitelbaum's conjecture.
Astérisque 331 (2010) 29-64.

40. pdf, published version.

Henri Darmon and Robert Pollack
The efficient calculation of Stark-Heegner points via overconvergent modular symbols
Israel Journal of Mathematics, 153 (2006), 319-354.

39. pdf

Henri Darmon and Adrian Iovita
The anticyclotomic main conjecture for supersingular elliptic curves.
Journal de l'Institut Mathématique de Jussieu, 7 Issue 2 (2008) 291-325.

38. original pdf or published version

Henri Darmon and Samit Dasgupta
Unités elliptiques, corps quadratiques réels, et une formule limite de Kronecker.
Proceedings de la Troisième Conférence Internationale de Théorie des Nombres Quebec-Maroc, Mai 2003, Casablanca-Marrakech.
Annales des sciences mathématiques du Québec, 28 no. 1-2, 77-88 (2005).

37. pdf, published version.

Henri Darmon and Samit Dasgupta
Elliptic units for real quadratic fields
Annals of Mathematics (2) 163 (2006), no. 1, 301-346.

36. pdf

Henri Darmon
Rational points on modular elliptic curves
CBMS Regional Conference Series in Mathematics, 101. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2004.

35. pdf

Henri Darmon and Adam Logan
Heegner points and Hilbert modular forms
Algebraic number theory and related topics, RIMS Kokyuroku 1324, May 2003, 153-160.

34. pdf, published version.

Henri Darmon and Adam Logan
Periods of Hilbert modular forms and rational points on elliptic curves
International Mathematics Research Notices (2003) no. 40, 2153-2180.

33. pdf

Henri Darmon
Heegner points and elliptic curves of large rank over function fields.
Proceedings of an MSRI workshop on special values of Rankin L-series, H. Darmon and S. Zhang, eds., November 2004. pp. 317-322.

32. pdf, published version.

Massimo Bertolini and Henri Darmon
A Birch and Swinnerton-Dyer conjecture for the Mazur-Tate circle pairing.
Duke Math Journal (2004) 122 No 1, 181-204.

31. pdf

Massimo Bertolini, Henri Darmon and Peter Green
Periods and points attached to quadratic algebras.
Proceedings of an MSRI workshop on special values of Rankin L-series, H. Darmon and S. Zhang, eds., November 2004. 323-382.

30. pdf, published version.

Henri Darmon and Peter Green
Elliptic curves and class fields of real quadratic fields: algorithms and evidence.
Experimental Mathematics, 11:1 (2002) 37-55.

29. pdf

Massimo Bertolini and Henri Darmon
The p-adic L-functions of modular elliptic curves
in 2001 and Beyond, Springer-Verlag, 2001.

28. pdf, published version.

Henri Darmon
Integration on H_px H and arithmetic applications
Annals of Mathematics 154 (2001) 589-639.

27. pdf, published version.

Massimo Bertolini and Henri Darmon
Iwasawa's Main Conjecture for Elliptic Curves over Anticyclotomic Z_p-extensions
Annals of Mathematics, 162 (2005) 1-64.

26. pdf, published version.

Massimo Bertolini, Henri Darmon, Adrian Iovita, and Michael Spiess
Teitelbaum's exceptional zero conjecture in the anticyclotomic setting
American Journal of Mathematics 124 (2002) 411-449.

25. pdf, published version.

Henri Darmon
Modularity of fibres in rigid local systems
Annals of Mathematics 149 (1999) 1079-1086.

24. pdf, published version.

Henri Darmon
Rigid local systems, Hilbert modular forms, and Fermat's Last Theorem
Duke Math Journal 102 (2000) 413-449.

23. pdf

Massimo Bertolini and Henri Darmon
Non-triviality of families of Heegner points and ranks of Selmer groups over anticyclotomic towers
Journal of the Ramanujan Mathematical Society 13 (1998) no. 1, 15-24.

22. pdf, published version.

Henri Darmon and Jean-Francois Mestre
Courbes hyperelliptiques à multiplications réelles et une construction de Shih
Canadian Math Bulletin 43 (2000) 304-311.

21. pdf, published version.

Massimo Bertolini and Henri Darmon
Euler systems and Jochnowitz congruences
American Journal of Mathematics 121 (1999) 259-281.

20. pdf, published version.

Massimo Bertolini and Henri Darmon
p-adic periods, p-adic L-functions and the p-adic uniformization of Shimura curves
Duke Math Journal 98 (1999) 305-334.

19. pdf

Henri Darmon
Stark-Heegner points over real quadratic fields
Number theory (Tiruchirapalli, 1996) 41-69 Contemporary Mathematics 210, AMS, Providence, RI, 1998.

18. pdf, published version.

Henri Darmon and Loïc Merel
Winding quotients and some variants of Fermat's Last Theorem
Journal für die reine und angewandte Mathematik 490 (1997) 81-100.

17. pdf, published version.

Massimo Bertolini and Henri Darmon
Heegner points, p-adic L-functions and the Cerednik-Drinfeld uniformization
Inventiones Math 131 (1998) 453-491.

16. pdf, published version.

Massimo Bertolini and Henri Darmon, with an appendix by Bas Edixhoven
A rigid analytic Gross-Zagier formula and arithmetic applications
Annals of Mathematics 146 (1997) 111-147.

15. pdf, published version.

Massimo Bertolini and Henri Darmon
Heegner points on Mumford-Tate curves
Inventiones Math 126 (1996) 413-456.

14. pdf

Antal Balog, Henri Darmon and Ken Ono
Congruences for Fourier coefficients of half- integral weight modular forms and special values of L-functions
Analytic number theory: Proceedings of a Conference in Honor of Heini Halberstam, Volume 1, 105-128, 1996, Birkhauser, Boston.

13. pdf, published version.

Massimo Bertolini and Henri Darmon
Derived p-adic heights
American Journal of Mathematics 117 (1995) 1-38.

12. pdf, published version.

Henri Darmon and Andrew Granville
On the equations x^p+y^q=z^r and z^m=f(x,y)
Bulletin of the London Mathematical Society, no 129, 27 part 6, November 1995, pp. 513-544.

11. pdf

Massimo Bertolini and Henri Darmon
Derived heights and generalized Mazur-Tate regulators
Duke Math Journal 76 No. 1 (1994) pp. 75-111.

10. pdf

Henri Darmon
The equation x⁴-y⁴=z^p
C.R. Math. Rep. Acad. Sci. Canada. XV No. 6 (1993) pp. 286-290.

9. pdf, published version.

Henri Darmon
Thaine's method for circular units and a conjecture of Gross
Canadian Journal of Mathematics Vol. 47 (2) (1995) pp. 302-317.

8. pdf

Henri Darmon
On the equations xⁿ+yⁿ=z² and xⁿ+yⁿ=z³
Duke International Mathematics Research Notices 72 No. 1 (1993) pp. 263-274.

7. pdf

Henri Darmon
Heegner points, Heegner cycles, and congruences
In "Elliptic curves and related topics", CRM proceedings and lecture notes vol. 4, H. Kisilevsky and M. Ram Murty eds. (1992) pp. 45-60.

6. pdf.

Henri Darmon
Euler systems and refined conjectures of Birch and Swinnerton-Dyer type
Contemporary Mathematics 165 (1994) pp. 265-276.

5. pdf, published version.

Henri Darmon
A refined conjecture of Mazur-Tate type for Heegner points
Inventiones Math 110 (1992) pp.123-146.

4. pdf, published version.

Massimo Bertolini and Henri Darmon
Kolyvagin's descent and Mordell-Weil groups over ring class fields
Journal für die reine und angewandte Mathematik 412 (1990) pp. 63-74.

3. pdf, published version.

Henri Darmon
Note on a polynomial of Emma Lehmer
Mathematics of Computation 56 No. 194, April 1991, pp. 795- 800.

2. published version.

Henri Darmon and John McKay
A continued fraction and permutations with fixed points.
American Mathematical Monthly 98, No. 1, January 1991, pp. 25-27.

1. pdf, published version.

Henri Darmon and David Ford
Computational Verification of M₁₁ and M₁₂ as Galois groups over Q
Communications in Algebra 17 No.12 (1989) p. 2941-2944.

Tributes

3. pdf, published version, further material.

Henri Darmon
The work of Barry Mazur.
Laudatio for the 2022 Chern Medal, delivered at the 2022 International Congress of Mathematicians, Helsinki.
Proceedings of the 2022 International Congress of Mathematicians, Vol. 1, pp. 118-141. EMS Press, Berlin, 2023.

2. pdf.

Henri Darmon
Reminiscences of Dick Gross.
Celebratio Mathematica, special issue dedicated to Dick Gross.

1. pdf, video.

Henri Darmon
Andrew Wiles's Marvelous Proof.
Public lecture on the occasion of Andrew Wiles receiving the 2016 Abel Prize, delivered at the Abel Prize ceremonies, Oslo.
Notices of the AMS, March 2017, 209-216.

Unrefereed Articles

15. pdf.

Henri Darmon
Rigid meromorphic cocycles.
Oberwolfach reports, 2019
Modular forms, December 13-18, 2019.

14. pdf.

Henri Darmon
Euler systems and the Birch and Swinnerton-Dyer conjecture.
Oberwolfach reports, Report No. 32/2014
Algebraische Zahlentheorie, July 6-12, 2014.

13. pdf.

Henri Darmon
Cycles on modular varieties and rational points on elliptic curves
Oberwolfach reports, Volume 6, Issue 3, 2009, 1843-1920
Explicit Methods in Number Theory.

12. pdf.

Henri Darmon
Rational points on curves
Proceedings of the Clay Summer School on the arithmetic of curves, surfaces, and higher-dimensional varieties.
Clay Mathematics Proceedings, Volume 8, (2009) 7-55.

11. pdf

Henri Darmon
Review of the book "Automoprhic forms and L-series" by Cogdell, Kim and Murty.
Fields Institute publications.

10. pdf

Henri Darmon and Shou-Wu Zhang
Preface to the Proceedings volume "Heegner points and Rankin L-series"
Cambridge University Press.

9. pdf

Henri Darmon
A fourteenth lecture on Fermat's Last Theorem
Number theory, 103-115, CRM Proc. Lecture Notes 36 Amer. Math. Soc., Providence, RI, 2004.

8. pdf

Henri Darmon
Review of "Euler Systems" by Karl Rubin
Bull. Amer. Math. Soc. 39 (2002), 407-414.

7. pdf

Henri Darmon
The Shimura-Taniyama Conjecture
Article in the Encyclopedia of Mathematics (1999).

6. pdf

Henri Darmon
Elliptic curves and p-adic uniformisation
CMS notes, March 1999, 8-16.

5. pdf

Henri Darmon, Fred Diamond and Richard Taylor
Fermat's Last Theorem
Current Developments in Mathematics 1, 1995, International Press, pp. 1-157.
Reprinted in
Elliptic curves, modular forms & Fermat's last theorem (Hong Kong, 1993), 2-140, International Press, Cambridge, MA, 1997.

4. pdf

Henri Darmon
Faltings plus epsilon, Wiles plus epsilon, and the generalized Fermat equation
C.R. Math. Rep. Acad. Sci. Canada Vol. 19 (1), 1997 pp. 3-14.

3. pdf

Henri Darmon
Wiles' theorem and the arithmetic of elliptic curves
Modular forms and Fermat's last theorem (Boston, MA, 1995), 549-569, Springer, New York, 1997.

2. pdf.

Henri Darmon
Serre's Conjectures
CICMA preprint; in "Seminar on Fermat's Last Theorem", V. Kumar Murty ed., CMS conference proceedings Volume 17, pp. 135-155.

1. pdf.

Henri Darmon
The Shimura- Taniyama conjecture (d'après Wiles)
(in Russian) Uspekhi Mat. Nauk 50 no. 3 (1995)(303), 33-82.
(English version: Russian Math Surveys 50 No 3 (1995) pp. 503-549.)

Popular Surveys

5. pdf

Henri Darmon
De la conjecture de Fermat au théorème.
Entretien accordé au magazine ``La Recherche", 2020.

4. pdf

Henri Darmon
Taureaux, internet et quanta: l'arithmétique des très grands nombres
Un apercu de la recherche à l'occasion de l'année mathématique mondiale, produit par l'ISM et l'AMQ.

3. pdf

Henri Darmon
Le Dernier Théorème de Fermat
Encart dans Québec Science. Eté 2000.

2 . pdf

Henri Darmon
A Proof of the Full Shimura-Taniyama-Weil Conjecture is Announced
Notices of the AMS, December 1999, Vol 46, No. 11, 1397-1401.

French translation: pdf
La Conjecture de Shimura-Taniyama-Weil est enfin Démontrée
Gazette des Mathématiciens, Société Mathématique de France.

1. pdf

Henri Darmon et Claude Levesque
Sommes infinies, équations diophantiennes et le dernier théorème de Fermat
Comptes-rendus du Colloque des Sciences Mathématiques du Québec, Lévis, Octobre 1995; et
Gazette des Sciences Mathématiques du Québec, Volume XVIII, Numéro 1, Avril1996 (numéro dédié à la mémoire de Carl Herz).

English translation: pdf
Infinite sums, Diophantine equations, and Fermat's Last Theorem
Number theoretic methods (Iizuka, 2001), 73-95, Dev. Math., 8, Kluwer Acad. Publ., Dordrecht, 2002.

PhD Thesis

Henri Darmon
Refined class number formulas for derivatives of L-series
PhD. thesis, Harvard, 1991, under the direction of B.H. Gross.
pdf

Miscellaneous

Jean-Pierre Serre
Topics in Galois Theory
Based on a course taught by J-P. Serre at Harvard in 1989, and notes taken by Henri Darmon.
Research Notes in Mathematics, Volume 1, Jones and Bartlett Publishers, 1992.