Title:

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

## 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 Thesis (Masters) Kazi, Ananyo University of Milan, Concordia University M. Sc. Mathematics 15 July 2019 Andreatta, Fabrizio and Iovita, Adrian 985661 Ananyo Kazi 15 Nov 2019 16:13 15 Nov 2019 16:13
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