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p-adic Modular Forms

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p-adic Modular Forms

Kazi, Ananyo (2019) p-adic Modular Forms. Masters thesis, University of Milan, Concordia University.

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Abstract

We study the approach of N.M. Katz to define $p$-adic modular forms, first as sections of tensor powers of the sheaf of invariant differentials on the formal ordinary locus and then as functions on the Katz modula satisfying certain transformation properties under the action of a Galois group, depending on the weight. Next we study the Igusa tower and the big Igusa tower and describe an action of the multiplicative formal group on the Igusa tower which restricts to an action on the Katz tower. We show, that one gets back the $\theta$-operator of Serre by differentiating this action.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Kazi, Ananyo
Institution:University of Milan, Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:15 July 2019
Thesis Supervisor(s):Andreatta, Fabrizio and Iovita, Adrian
ID Code:985661
Deposited By: Ananyo Kazi
Deposited On:15 Nov 2019 16:13
Last Modified:15 Nov 2019 16:13
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