Singularities and vanishing cycles in number theory over function fields

Abstract

This article is an overview of the vanishing cycles method in number theory over function fields. We first explain how this works in detail in a toy example, and then give three examples which are relevant to current research. The focus will be a general explanation of which sorts of problems this method can be applied to.

arXiv comment34 pages, to appear in PIMS Workshop on Arithmetic Topology conference proceedings