We obtain new results on the geometry of Hilbert modular varieties in positive characteristic and morphisms between them. Using these results and methods of rigid geometry, we develop a theory of canonical subgroups for abelian varieties with real multiplication.
Nous obtenons des résultats nouveaux sur la géométrie des variétés modulaires de Hilbert en caractéristique positive et sur les morphismes entre celles-ci. Grâce à ces résultats et des méthodes de géométrie rigide, nous développons une théorie des sous-groupes canoniques pour les variétés abéliennes à multiplication réelle.
Accepted:
Published online:
Eyal Z. Goren 1; Payman L. Kassaei 2
@article{CRMATH_2009__347_17-18_985_0, author = {Eyal Z. Goren and Payman L. Kassaei}, title = {Canonical subgroups over {Hilbert} modular varieties}, journal = {Comptes Rendus. Math\'ematique}, pages = {985--990}, publisher = {Elsevier}, volume = {347}, number = {17-18}, year = {2009}, doi = {10.1016/j.crma.2009.07.008}, language = {en}, }
Eyal Z. Goren; Payman L. Kassaei. Canonical subgroups over Hilbert modular varieties. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 985-990. doi : 10.1016/j.crma.2009.07.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.07.008/
[1] Sous-groupes canoniques et cycles évanescents p-adiques pour les variétés abéliennes, Publ. Math. Inst. Hautes Études Sci., Volume 99 (2004), pp. 117-162
[2] The canonical subgroup for families of abelian varieties, Compos. Math., Volume 143 (2007) no. 3, pp. 566-602
[3] Companion forms and weight one forms, Ann. of Math. (2), Volume 149 (1999) no. 3, pp. 905-919
[4] B. Conrad, Higher-level canonical subgroups in abelian varieties, preprint
[5] Singularités des espaces de modules de Hilbert, en les caractéristiques divisant le discriminant, Compositio Math., Volume 90 (1994) no. 1, pp. 59-79
[6] Application de Hodge–Tate duale d'un groupe de Lubin–Tate, immeuble de Bruhat–Tits du groupe linéaire et filtrations de ramification, Duke Math. J., Volume 140 (2007) no. 3, pp. 499-590
[7] Hasse invariants for Hilbert modular varieties, Israel J. Math., Volume 122 (2001), pp. 157-174
[8] The canonical subgroup: A “subgroup-free” approach, Comment. Math. Helv., Volume 81 (2006) no. 3, pp. 617-641
[9] Stratifications of Hilbert modular varieties, J. Algebraic Geom., Volume 9 (2000) no. 1, pp. 111-154
[10] A gluing lemma and overconvergent modular forms, Duke Math. J., Volume 132 (2006) no. 3, pp. 509-529
[11] Overconvergence, analytic continuation, and classicality: The case of curves, J. Reine Angew. Math., Volume 631 (2009), pp. 109-139
[12] N.M. Katz, p-Adic properties of modular schemes and modular forms, in: Modular Functions of One Variable III, in: Lecture Notes in Mathematics, vol. 350, 1973, pp. 69–190
[13] Overconvergent Hilbert modular forms, Amer. J. Math., Volume 127 (2005) no. 4, pp. 735-783
[14] On the reduction of the Hilbert–Blumenthal-moduli scheme with -level structure, Forum Math., Volume 9 (1997) no. 4, pp. 405-455
[15] Y. Tian, Canonical subgroups of Barsotti–Tate groups, Ann. of Math., in press
Cited by Sources:
Comments - Policy