We review the construction of analytic families of Siegel modular cuspforms based on the notion of overconvergent modular forms of p-adic weight. We then present recent developments on the following subjects: the halo conjecture, the construction of p-adic L-functions, and the modularity of irregular motives.
p-Adic variation of automorphic sheaves / F. Andreatta, A. Iovita, V. Pilloni - In: Proceedings of the International Congress of Mathematicians (ICM 2018). 1 / [a cura di] B. Sirakov, P. Ney de Souza, M. Viana. - [s.l] : World Scientific, 2019. - ISBN 9789813272873. - pp. 291-318 (( convegno ICM tenutosi a Rio de janeiro nel 2018 [10.1142/11060].
p-Adic variation of automorphic sheaves
F. Andreatta;
2019
Abstract
We review the construction of analytic families of Siegel modular cuspforms based on the notion of overconvergent modular forms of p-adic weight. We then present recent developments on the following subjects: the halo conjecture, the construction of p-adic L-functions, and the modularity of irregular motives.
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