P-Adic families of Siegel modular cuspforms

TL;DR

This paper demonstrates that finite slope Siegel cusp forms of genus g can be p-adically deformed over a g-dimensional weight space, using families of sheaves of overconvergent modular forms.

Contribution

It introduces a method to p-adically deform finite slope Siegel cusp forms of genus g over a g-dimensional weight space, expanding the understanding of their p-adic variation.

Findings

Finite slope Siegel cusp forms can be p-adically deformed.

Construction of sheaves of locally analytic overconvergent modular forms.

Deformation occurs over a g-dimensional weight space.

Abstract

Let p be an odd prime and g an integer greater or equal to 2. We prove that a finite slope Siegel cuspidal eigenform of genus g can be p-adically deformed over the g-dimensional weight space. The proof of this result relies on the construction of a family of sheaves of locally analytic overconvergent modular forms.