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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

5 votes

Ideals in the I-adic completion of a ring

Since irreducibility of noetherian schemes is not local for the etale topology, one gets zillions of noetherian counterexamples from irreducible varieties which are not "analytically irreducible". To …
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5 votes
Accepted

Is this formally étale morphism of schemes an isomorphism?

[I originally gave what I thought to be a counterexample in the affine case, but I realized it violates universal schematic dominance, so below I give a non-qc counterexample that was originally a com …
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6 votes
Accepted

"Unramified" extension of DVRs and permanence of excellence

No. Let $R'$ be any non-excellent dvr whatsoever, hence of equicharacteristic $p > 0$, and let $t \in R'$ be a uniformizer. Let $R = \mathbf{F}_p[t]_{(t)}$. The local inclusion $R \hookrightarrow R'$ …
4 votes

Minimal fields of isomorphism for varieties

This question is most "reasonable" when $V$ is projective, since at least then the automorphism functor is represented by a (locally finite type) $K$-scheme $G_V := {\rm{Aut}}_{V/K}$ and so one can tr …
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