# Small projective spaces and Stillman uniformity for sheaves

## TL;DR

This paper extends the small subalgebra theorem to sheaves on projective space and proves a version of Stillman's Conjecture for their cohomology tables, using advanced algebraic tools.

## Contribution

It introduces a sheaf-theoretic analogue of the small subalgebra theorem and establishes Stillman's Conjecture in this new context, leveraging GL-noetherianity and BGG correspondence.

## Key findings

- Proved a sheaf version of the small subalgebra theorem.
- Established Stillman's Conjecture for sheaf cohomology tables.
- Utilized Draisma's GL-noetherianity and BGG correspondence in proofs.

## Abstract

We prove an analogue of Ananyan--Hochster's small subalgebra theorem in the context of sheaves on projective space, and deduce from this a version of Stillman's Conjecture for cohomology tables of sheaves. The main tools in the proof are Draisma's GL-noetherianity theorem and the BGG correspondence.