# Derived equivalences for Symplectic reflection algebras

## TL;DR

This paper explores derived equivalences in Symplectic reflection algebras, establishing a localization theorem linking module categories to coherent sheaves on quantized terminalizations, with applications to inequalities and wall crossing functors.

## Contribution

It introduces a derived localization theorem for Symplectic reflection algebras and constructs Procesi sheaves on terminalizations, advancing understanding of their module categories.

## Key findings

- Established derived localization theorem for Symplectic reflection algebras
- Constructed Procesi sheaves on symplectic terminalizations
- Applied results to Bernstein inequality and wall crossing functors

## Abstract

In this paper we study derived equivalences for Symplectic reflection algebras. We establish a version of the derived localization theorem between categories of modules over Symplectic reflection algebras and categories of coherent sheaves over quantizations of Q-factorial terminalizations of the symplectic quotient singularities. To do this we construct a Procesi sheaf on the terminalization and show that the quantizations of the terminalization are simple sheaves of algebras. We will also sketch some applications: to the generalized Bernstein inequality and to perversity of wall crossing functors.