Big polynomial rings with imperfect coefficient fields

Abstract

We previously showed that the inverse limit of standard-graded polynomial rings with perfect coefficient field is a polynomial ring, in an uncountable number of variables. In this paper, we show that the same result holds with arbitrary coefficient field. We also prove an analogous result for ultraproducts of polynomial rings.

20 pages

References in corpus (3)

• Big polynomial rings and Stillman's conjecture
• Polynomials and tensors of bounded strength
• Stillman's conjecture via generic initial ideals

Cited by in corpus (7)

• Big polynomial rings and Stillman's conjecture
• Universality of high-strength tensors
• Cubics in 10 variables vs. cubics in 1000 variables: Uniformity phenomena for bounded degree polynomials
• The set of forms with bounded strength is not closed
• Strength conditions, small subalgebras, and Stillman bounds in degree $\le 4$
• Strength and Hartshorne's Conjecture in high degree
• Free limits of free algebras