Geometric and p-adic Modular Forms of Half-Integral Weight
[Formes modulaires géometriques et p-adiques des poids demi-entiers]
Annales de l'Institut Fourier, Tome 56 (2006) no. 3, pp. 599-624.

Nous nous proposons ici de présenter un formalisme géométrique ayant pour but l’étude des formes modulaires des poids demi-entiers. Ce formalisme est mis à contribution pour définir les formes modulaires p-adiques des poids demi-entiers, et dans la construction des opérateurs de Hecke p-adiques.

In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define p-adic modular forms of half-integral weight and to construct p-adic Hecke operators.

DOI : 10.5802/aif.2195
Classification : 11F33, 11F37
Keywords: Modular forms of half-integral weight, $p$-adic modular forms
Mot clés : formes modulaires des poids demi-entiers, formes modulaires p-adiques
Ramsey, Nick 1

1 University of Michigan Department of Mathematics 2074 East Hall 530 Church Street Ann Arbor, MI 48109-1043 (USA)
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Ramsey, Nick. Geometric and $p$-adic Modular Forms of Half-Integral Weight. Annales de l'Institut Fourier, Tome 56 (2006) no. 3, pp. 599-624. doi : 10.5802/aif.2195. http://www.numdam.org/articles/10.5802/aif.2195/

[1] Buzzard, Kevin Analytic continuation of overconvergent eigenforms, J. Amer. Math. Soc., Volume 16 (2003) no. 1, pp. 29-55 | DOI | MR | Zbl

[2] Coleman, R.; Mazur, B. The eigencurve, Galois representations in arithmetic algebraic geometry (Durham, 1996) (London Math. Soc. Lecture Note Ser.), Volume 254, Cambridge Univ. Press, Cambridge, 1998, pp. 1-113 | MR | Zbl

[3] Coleman, Robert F. p-adic Banach spaces and families of modular forms, Invent. Math., Volume 127 (1997) no. 3, pp. 417-479 | DOI | MR | Zbl

[4] Katz, Nicholas M. p-adic properties of modular schemes and modular forms, Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) (Lecture Notes in Mathematics), Volume 350, Springer, Berlin, 1973, pp. 69-190 | MR | Zbl

[5] Katz, Nicholas M.; Mazur, Barry Arithmetic moduli of elliptic curves, Annals of Mathematics Studies, 108, Princeton University Press, Princeton, NJ, 1985 | MR | Zbl

[6] Ramsey, Nicholas The half-integral weight eigencurve (in preparation)

[7] Ramsey, Nicholas Geometric and p-adic Modular Forms of Half-Integral Weight, Harvard University Thesis (2004) (Ph. D. Thesis)

[8] Shimura, Goro On modular forms of half integral weight, Ann. of Math. (2), Volume 97 (1973), pp. 440-481 | DOI | MR | Zbl

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