Geometric and p-adic Modular Forms of Half-Integral Weight
Annales de l'Institut Fourier, Volume 56 (2006) no. 3, pp. 599-624.

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.

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.

Received:
Accepted:
DOI: 10.5802/aif.2195
Classification: 11F33,  11F37
Keywords: Modular forms of half-integral weight, p-adic modular forms
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Ramsey, Nick. Geometric and $p$-adic Modular Forms of Half-Integral Weight. Annales de l'Institut Fourier, Volume 56 (2006) no. 3, pp. 599-624. doi : 10.5802/aif.2195. https://aif.centre-mersenne.org/articles/10.5802/aif.2195/

[1] Buzzard, Kevin Analytic continuation of overconvergent eigenforms, J. Amer. Math. Soc., Tome 16 (2003) no. 1, pp. 29-55 | Article | MR: 1937198 | Zbl: 1076.11029

[2] Coleman, R.; Mazur, B. The eigencurve, Galois representations in arithmetic algebraic geometry (Durham, 1996) (London Math. Soc. Lecture Note Ser.) Tome 254, Cambridge Univ. Press, Cambridge, 1998, pp. 1-113 | MR: 1696485 | Zbl: 0932.11030

[3] Coleman, Robert F. p-adic Banach spaces and families of modular forms, Invent. Math., Tome 127 (1997) no. 3, pp. 417-479 | Article | MR: 1431135 | Zbl: 0918.11026

[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) Tome 350, Springer, Berlin, 1973, pp. 69-190 | MR: 447119 | Zbl: 0271.10033

[5] Katz, Nicholas M.; Mazur, Barry Arithmetic moduli of elliptic curves, Annals of Mathematics Studies, Tome 108, Princeton University Press, Princeton, NJ, 1985 | MR: 772569 | Zbl: 0576.14026

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

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

[8] Shimura, Goro On modular forms of half integral weight, Ann. of Math. (2), Tome 97 (1973), pp. 440-481 | Article | MR: 332663 | Zbl: 0266.10022

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