Publications                                       
back to Goren's webpage

Papers

• Eyal Z. Goren: On Certain Reduction Problems Concerning Abelian Surfaces, Manuscripta Math. 94 (1997), 33--43.
• E. De Shalit and E.Z. Goren: On special values of theta functions of genus two, Annales Inst. Fourier 47, 3 (1997), 775--799.
• E. Bachmat and E. Z. Goren: On the non ordinary locus in Hilbert-Blumenthal surfaces, Math. Annalen, 313 (1999) 3, 475-506.
• E. Z. Goren and F. Oort: Stratifications of Hilbert modular varieties, J. Algebraic Geom. 9(2000), 111-154.
• E. Z. Goren: Hasse invariants for Hilbert modular varieties, Israel J. Math. 122 (2001), 157-174.
• E. Z. Goren: Hilbert modular varieties in positive characteristic, The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), 283--303, CRM Proc. Lecture Notes, 24, Amer. Math. Soc., Providence, RI, 2000.
• E. Z. Goren: Hilbert modular forms modulo p^m -- the unramified case. J. Number Theory  90 (2001), no. 2, 341--375.
• F. Andreatta and E. Z. Goren: Hilbert modular forms: mod p and p-adic aspects.  Mem. Amer. Math. Soc. 173 (2005), no. 819, vi+100 pp.
• F. Andreatta and E. Z. Goren: Geometry of Hilbert modular varieties over totally ramified primes. Internat. Math. Res. Notices 33 (2003), 1785-1835.
• F. Andreatta and E. Z. Goren: Hilbert modular varieties of low dimension. In Geometric aspects of Dwork theory. Vol. I, II, 113--175, Walter de Gruyter GmbH & Co. KG, Berlin, 2004. Alan Adolphson, Francesco Baldassarri, Pierre Berthelot, Nicholas Katz, and Francois Loeser (Eds.).
• E. Z. Goren and K. Lauter: Class invariants for quartic CM fields. Annales Inst. Fourier 57, 2 (2007), p.457-480.
• E. Z. Goren and Payman L Kassaei: The canonical subgroup: a "subgroup-free" approach. Comm. Math. Helv., Volume 81 (3) (2006), 617-641.
• E. Z. Goren and K. Lauter: Evil primes and superspecial moduli. Int. Math. Res. Not. 2006, Art. ID 53864, 19 pp.
• D. X. Charles, E. Z. Goren and K. E. Lauter: Families of Ramanujan graphs and quaternion algebras. Groups and symmetries, 53--80, CRM Proc. Lecture Notes, 47, Amer. Math. Soc., Providence, RI, 2009, Special AMS-CRM volume in honor of John McKay.
• D. X. Charles, E. Z. Goren and K. E. Lauter: Cryptographic hash functions from expander graphs.  J. Cryptol. (2009) 22: 93–113
  DOI: 10.1007/s00145-007-9002-x. What's that all about? See the beautiful paper by Dana Mackenzie Cryptologists Cook Up Some Hash for New 'Bake-Off' (14 March 2008) Science 319 (5869), 1480-1. [DOI: 10.1126/science.319.5869.1480]
• E. Z. Goren and K. E. Lauter. The distance between superspecial abelian varieties with real multiplication. J. Number Theory 129, No. 6, 1562-1578 (2009).
• E. Z. Goren and Payman L Kassaei: Canonical subgroups over Hilbert modular varieties. C. R. Acad. Sci. Paris, Ser. I 347 (2009) 985-990.
• E. Z. Goren and Payman L Kassaei: Canonical subgroups over Hilbert modular varieties. J. Reine Angew. Math. (Crelle's Journal). 63 pp. 2011. DOI: 10.1515/CRELLE.2011.149
• E. Z. Goren and Kristin E. Lauter: Genus 2 curves with complex multiplication, Int. Math. Res. Not. 2011, 75 pages. doi:10.1093/imrn/rnr052
• E. Z. Goren and Kristin E. Lauter: A Gross-Zagier formula for quaternion algebras over totally real fields. ANT, Volume 7, no. 6, 2013, pp. 1405-1450. 
• E. Z. Goren: Algebraic groups, representations and invariant theory. 24 pages. Submitted to the CRM proceedings of a Summer School "Counting Arithmetic Objects".
• E. De Shalit and E. Z. Goren: supersingular curves on Picard modular surfaces modulo an inert prime.  J. Number Theory 171 (2017), 391–421.
• E. De Shalit and E. Z. Goren: A theta operator on Picard modular forms.  Res. Math. Sci. 3 (2016), Paper No. 28, 65 pp. (a special volume in honor of Robert F. Coleman).
• F. Andreatta, E. Z. Goren, B. Howard and K. Madapusi Pera: Height pairings on orthogonal Shimura varieties. Compositio Math. 153 (2017), 474-534.
• F. Andreatta, E. Z. Goren, B. Howard and K. Madapusi Pera: Faltings heights of abelian varieties with complex multiplication. Annals of Math., 187 (2018), 1 - 141.
• E. De Shalit and E. Z. Goren: On the bad reduction of certain U(2, 1) Shimura varieties. In Geometry, Algebra, Number Theory, and Their Information Technology Applications,Toronto, Canada, June, 2016, and Kozhikode, India, August, 2016.  Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 251), 2018, pages 81-152. arXiv:1703.05720
• E. De Shalit and E. Z. Goren: Foliations on unitary Shimura varieties in positive characteristic. Compos. Math. 154 (2018), no. 11, 2267–2304. arXiv: 1707.08102
• E. Z. Goren and Payman L Kassaei: p-adic dynamics of Hecke operators on modular curves. JTNB, Tome 33, no 2 (2021), p. 387-431.
• E. De Shalit and E. Z. Goren: Theta operators on unitary Shimura varieties. Algebra & Number Theory (ANT), Vol. 13 (2019), No. 8, 1829–1877, DOI: 10.2140/ant.2019.13.1829   arXiv:1712.06969
• E. De Shalit and E. Z. Goren: Foliations on Shimura varieties in positive characteristic. Published electronically in J. Algebraic Geometry September 2023, 54 pp., https://doi.org/10.1090/jag/820 (arXiv:2205.00702)
• Eyal Z. Goren and Jonathan Love: On elements of prescribed norm in maximal orders of a quaternion algebra. 28 pp. Canad. J. Math. November 2024, arXiv:2307.16828 or Journal version
• Eyal Z. Goren and Jonathan Love: Supersingular elliptic curves, quaternion algebras and applications to cryptography. NATO Science for Peace and Security Series - D: Information and Communication Security, Volume 66: Abelian Surfaces and Isogeny-based Cryptography, 2025, 123 - 200.
• Kirsten Eisenträger, Eyal Z. Goren, Annamaria Iezzi, Harun Kir, Eda Kirimli, Jonathan R. Love, William E. Mahaney, Jennifer Park and Maria Sabitova: Generating sets for maximal orders in rational quaternion algebras. 48 pp. arXiv:2610.10139
• F. Andreatta and Eyal Z. Goren: Foliations on abelian surfaces in positive characteristic, 34 pp. https://arxiv.org/abs/2610.32975

Books

• Lectures on Hilbert Modular Varieties and Modular Forms. (With the assistance of M.-H. Nicole). 270 pp. CRM Monograph Series CRMM/14.
• Number Theory: Proceedings of the Canadian Number Theory Association 7 meeting. Montreal, 2002. H. Kisilevsky and E. Z. Goren, (Eds). CRM Proceedings and  Lecture Notes, Vol. 36, American Mathematical Society 2004.

Thesis

• E.Z. Goren: Units in abelian extensions of cm fields of degree four, Hebrew Univerity of Jerusalem 1996, xii + 102 + ix pages (Advisor: E. De Shalit).

Preprints

• E.Z. Goren: A note on vanishing properties of certain theta constants of genus 2, Landau Center, Preprint No. 15 (1995/6), 11 pages. DVI file or PS file. 
• E.Z. Goren: Quasi-symmetric line bundles on abelian varieties, Max Planck Inst, Preprint 95-106 (1995), 67 pages.

Lectures

• Quaternions and Arithmetic (Colloquium lecture)
• Class invariants for genus two by Eyal Goren and Kristin Lauter: Part I, Part II, the 4th Spring Conference on Modular Forms and Related Topics, Hamana Lake, Hamamatsu, Japan, February 5-9, 2007.
• Canonical Subgroups over Hilbert Modular Varieties. Minerva school of p-adic methods in arithmetic algebraic geometry. March 29 - April 7, 2009, and  Conference in Arithmetic Geometry in honor of Thomas Zink, Bielefeld June 14-19, 2009.
• 3 Lectures in the Summer school "Automorphic forms and L-functions: computational aspects" -- S\'eminaire de Math\'ematiques Sup\'erieures. June 22- July 3, 2009, CRM, Montreal.
• A lecture for the McGill math undergradute society SUMS on  Lattices. October 19, 2009, and to the McGill Winter School, January 8, 2010.
• A lecture at Vanier College, September 23, 2011, on Sums of Squares.
• A lecture on Algebraic groups at SMS - Summer school on Bhargava's work, June 2014, CRM Montreal.