Generalizations of Stillman's conjecture via twisted commutative algebras

Abstract

Combining recent results on noetherianity of twisted commutative algebras by Draisma and the resolution of Stillman's conjecture by Ananyan-Hochster, we prove a broad generalization of Stillman's conjecture. Our theorem yields an array of boundedness results in commutative algebra that only depend on the degrees of the generators of an ideal, and not the number of variables in the ambient polynomial ring.

16 pages

References in corpus (2)

• Big polynomial rings and Stillman's conjecture
• GL-equivariant modules over polynomial rings in infinitely many variables. II

Cited by in corpus (6)

• Big polynomial rings and Stillman's conjecture
• The geometry of polynomial representations
• Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum
• GL-algebras in positive characteristic I: the exterior algebra
• Semigroup Graded Stillman's Conjecture
• Stillman's question for twisted commutative algebras