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Big polynomial rings and Stillman's conjecture

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arxiv 1801.09852 v5 pith:UAUOGH6H submitted 2018-01-30 math.AC

Daniel Erman , Steven V Sam , Andrew Snowden This is my paper · ORCID
classification math.AC
keywords polynomialringsconjectureparticularstillmanalgebraananyan-hochstercertain
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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 results in commutative algebra. In particular, we give two new proofs of Stillman's conjecture. The first is similar to that of Ananyan-Hochster, though more streamlined; in particular, it establishes the existence of small subalgebras. The second proof is completely different, and relies on a recent noetherianity result of Draisma.

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  1. The fundamental theorems of invariant theory for linearly oligomorphic groups

    math.RT 2026-07 accept novelty 6.0 of 10

    The G-invariant symmetric forms on V^m for the automorphism group G of a universal homogeneous λ-space are freely generated by the contractions of the defining forms with Schur functors on k^m.

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