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Results tagged with ac.commutative-algebra
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user 73467
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
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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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 $\mathbf{Q}$ …
- 381
5
votes
Accepted
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 …
- 381