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

5 votes
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What is an excellent algebraic space?

Let $X$ be a Noetherian algebraic space. We say $X$ is quasi-excellent if the following equivalent conditions hold: (1) for every scheme $U$ and etale morphism $U \to X$ the scheme $U$ is quasi-excel …
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3 votes

Order of vanishing of an integer polynomial at a point

Over $\mathbf{Q}$ you can argue as follows. Case I. $a$ is the unique point where $f$ vanishes to high order. Then $a$ is invariant under $\text{Aut}(\mathbf{C})$ and hence defined over $\mathbf{Q}$ …
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2 votes

Transitivity of discriminant for flat algebras

This is a restatement of the beautiful answer by grghxy above in terms of dualizing modules. Namely, let $\omega_{A''/A}$ be the relative dualizing module, which in this case is just $Hom_A(A'', A)$. …
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