122 citations · 901 across the 71 of their papers we have counts for
4 papers · 2 filters
Cubics in 10 variables vs. cubics in 1000 variables: Uniformity phenomena for bounded degree polynomials
Daniel Erman, Steven V Sam, Andrew Snowden
Hilbert famously showed that polynomials in n variables are not too complicated, in various senses. For example, the Hilbert Syzygy Theorem shows that the process of resolving a mo…
Big polynomial rings with imperfect coefficient fields
Daniel Erman, Steven V Sam, Andrew Snowden
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…
Generalizations of Stillman's conjecture via twisted commutative algebras
Daniel Erman, Steven V Sam, Andrew Snowden
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 generalizatio…
Big polynomial rings and Stillman's conjecture
Daniel Erman, Steven V Sam, Andrew Snowden
The purpose of this paper is to prove that certain limits of polynomial rings are themselves polynomial rings, and show how this observation can be used to deduce some interesting…