Topological Noetherianity of polynomial functors (1705.01419v4)

Abstract: We prove that any finite-degree polynomial functor is topologically Noetherian. This theorem is motivated by the recent resolution of StiLLMan's conjecture and a recent Noetherianity proof for the space of cubics. Via work by Erman-Sam-Snowden, our theorem implies StiLLMan's conjecture and indeed boundedness of a wider class of invariants of ideals in polynomial rings with a fixed number of generators of prescribed degrees.