[Formes modulaires géometriques et -adiques des poids demi-entiers]
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 -adiques des poids demi-entiers, et dans la construction des opérateurs de Hecke -adiques.
In this paper we introduce a geometric formalism for studying modular forms of half-integral weight. We then use this formalism to define -adic modular forms of half-integral weight and to construct -adic Hecke operators.
Keywords: Modular forms of half-integral weight, $p$-adic modular forms
Mot clés : formes modulaires des poids demi-entiers, formes modulaires p-adiques
@article{AIF_2006__56_3_599_0,
author = {Ramsey, Nick},
title = {Geometric and $p$-adic {Modular} {Forms} of {Half-Integral} {Weight}},
journal = {Annales de l'Institut Fourier},
pages = {599--624},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {56},
number = {3},
year = {2006},
doi = {10.5802/aif.2195},
mrnumber = {2244225},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2195/}
}
TY - JOUR AU - Ramsey, Nick TI - Geometric and $p$-adic Modular Forms of Half-Integral Weight JO - Annales de l'Institut Fourier PY - 2006 SP - 599 EP - 624 VL - 56 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2195/ DO - 10.5802/aif.2195 LA - en ID - AIF_2006__56_3_599_0 ER -
%0 Journal Article %A Ramsey, Nick %T Geometric and $p$-adic Modular Forms of Half-Integral Weight %J Annales de l'Institut Fourier %D 2006 %P 599-624 %V 56 %N 3 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2195/ %R 10.5802/aif.2195 %G en %F AIF_2006__56_3_599_0
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] Analytic continuation of overconvergent eigenforms, J. Amer. Math. Soc., Volume 16 (2003) no. 1, pp. 29-55 | DOI | MR | Zbl
[2] 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] -adic Banach spaces and families of modular forms, Invent. Math., Volume 127 (1997) no. 3, pp. 417-479 | DOI | MR | Zbl
[4] -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] Arithmetic moduli of elliptic curves, Annals of Mathematics Studies, 108, Princeton University Press, Princeton, NJ, 1985 | MR | Zbl
[6] The half-integral weight eigencurve (in preparation)
[7] Geometric and -adic Modular Forms of Half-Integral Weight, Harvard University Thesis (2004) (Ph. D. Thesis)
[8] On modular forms of half integral weight, Ann. of Math. (2), Volume 97 (1973), pp. 440-481 | DOI | MR | Zbl
Cité par Sources :
