[McGill][Math.McGill]


Henri Darmon - Publications



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

Research Articles and Monographs


63. pdf.

Henri Darmon, Alan Lauder and Victor Rotger
Stark points and p-adic iterated integrals attached to modular forms of weight one.
Submitted.


62. pdf.

Henri Darmon and Victor Rotger.
Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-series.
Submitted.


61. pdf.

Henri Darmon and Victor Rotger
Diagonal cycles and Euler systems I: A p-adic Gross-Zagier formula.
Annales Scientifiques de l'Ecole Normale Supérieure, to appear.


60. 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.
Proceedings of the Durham Symposium on Galois representations and L-functions, to appear.


59. pdf.

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, to appear.


58. pdf.

Massimo Bertolini, Henri Darmon and Victor Rotger
Beilinson-Flach elements and Euler systems I: syntomic regulators and p-adic Rankin L-series.
Submitted.


57. pdf.

Massimo Bertolini, Henri Darmon and Kartik Prasanna.
p-adic L-functions and the coniveau filtration on Chow groups.
submitted.


56. pdf.

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, to appear.


55. pdf.

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,

Massimo Bertolini, Henri Darmon, and Kartik Prasanna
Generalised Heegner cycles and the complex Abel-Jacobi map.
in progress.


53. pdf.

Massimo Bertolini, Henri Darmon, and Kartik Prasanna
Chow-Heegner points on CM elliptic curves and values of p-adic L-functions.
IMRN, to appear.


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, 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,

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

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 (No. 320), p. 1-23, D. Burns, K. Buzzard, and J. Nekovar, eds.


43. pdf

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

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

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

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

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

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

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

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


27. pdf

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


26. pdf

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

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


24. pdf

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

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

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


20. pdf

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

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

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


16. pdf

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

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

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


12. pdf

Henri Darmon and Andrew Granville
On the equations xp+yq=zr and zm=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=zp
C.R. Math. Rep. Acad. Sci. Canada. XV No. 6 (1993) pp. 286-290.


9. pdf

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

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


4. pdf

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

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


2.

Henri Darmon and John McKay
Permutations with Fixed Point and a Continued Fraction
American Mathematical Monthly 98, No. 1, January 1991, pp. 25-27.


1. pdf

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





Expository Articles


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


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.


[McGill][Math.McGill]