Sur la noeth{\'e}rianit{\'e} locale des foncteurs polynomiaux

TL;DR

This paper proves that finitely-generated polynomial functors from finitely-generated projective modules over a finitely-generated ring to modules over a noetherian ring are noetherian and possess finitely-generated projective resolutions.

Contribution

It establishes the noetherianity and existence of finitely-generated projective resolutions for polynomial functors in this algebraic setting.

Findings

Finitely-generated polynomial functors are noetherian.

Such functors have finitely-generated projective resolutions.

Results hold over finitely-generated rings and noetherian rings.

Abstract

Let A be a finitely-generated commutative ring and k a noetherian commutative ring. We show that, in the category of functors from finitely-generated projective A-modules to k-modules, each finitely-generated polynomial functor is noetherian and has a finitely-generated projective resolution.