An equivariant Hilbert basis theorem

TL;DR

This paper extends the Hilbert basis theorem to equivariant algebraic geometry, showing that under a group action, certain noetherian properties are preserved in scheme morphisms.

Contribution

It introduces an equivariant version of the Hilbert basis theorem, establishing noetherianity preservation under group actions in algebraic geometry.

Findings

Proves that G-noetherianity of the base scheme implies G-noetherianity of the total space.

Extends classical Hilbert basis theorem to equivariant scheme morphisms.

Provides foundational results for equivariant algebraic geometry.

Abstract

We prove a version of the Hilbert basis theorem in the setting of equivariant algebraic geometry: given a group G acting on a finite type morphism of schemes X -> S, if S is topologically G-noetherian, then so is X.