Singularities and vanishing cycles in number theory over function fields

TL;DR

This paper reviews the vanishing cycles method in number theory over function fields, illustrating its application through examples and explaining its relevance to current research problems.

Contribution

It provides a comprehensive overview of the vanishing cycles technique in the context of number theory over function fields, including detailed explanations and relevant examples.

Findings

Demonstrates the application of vanishing cycles in specific number theory problems

Provides detailed toy example illustrating the method

Highlights the relevance of the method to current research

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.