Autoequivalences of the category of schemes

TL;DR

This paper proves that the only autoequivalence of the category of schemes of finite type over  is the trivial one, indicating the category's structural rigidity.

Contribution

It establishes the non-existence of non-trivial autoequivalences for schemes over , a significant rigidity result in algebraic geometry.

Findings

No non-trivial autoequivalence exists for schemes over 

The category's structure is uniquely determined up to trivial automorphisms

Supports the idea of categorical rigidity in algebraic geometry

Abstract

We prove that there is no non-trivial aoutoequvivalence of the categoryof schemes of finite type over $\mathbb{Q}$.