A proof of Grothendieck's base change theorem

TL;DR

This paper provides an elementary and concise proof of Grothendieck's base change theorem, which is fundamental in algebraic geometry for understanding how cohomology behaves under base change for flat coherent sheaves.

Contribution

It introduces a simplified and accessible proof of Grothendieck's base change theorem, making the result more approachable for researchers and students.

Findings

Proof is elementary and short

Cohomology of flat coherent sheaves behaves well under base change

Simplifies understanding of a key theorem in algebraic geometry

Abstract

We give an elementary short proof of Grothendieck's base change theorem for the cohomology of flat coherent sheaves.