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Results tagged with ac.commutative-algebra
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user 1528
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
1
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0
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The structure of symmetric powers of finite-dimensional local rings
Fix an algebraically closed field $k$ of arbitrary characteristic $p$ and let $R$ be a finite-dimensional local $k$-algebra (so in particular $R$ is Artinian and Noetherian). Let $S_n$ be the symmetri …
- 3,637
2
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1
answer
486
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On the divided power ring over the integers
Consider the divided-power ring $A := \mathbb Z \langle x_1, \ldots, x_n \rangle$ consisting of $\mathbb Z$-linear combinations of divided-power monomials of the form $x_1^{(a_1)} \cdots x_n^{(a_n)}$; …
- 3,637
3
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0
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On the associated graded ring to a section ring
Consider a nonsingular projective variety $X$ over an algebraically closed field $k$ and let $Y \subseteq X$ be a nonsingular closed subvariety. Let $\mathcal I \subseteq \mathcal O_X$ be the ideal sh …
- 3,637
7
votes
1
answer
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Smooth affine algebraic subgroups as complete intersections
Let's fix an algebraically closed field $k$ of arbitrary characteristic and a connected nonsingular affine algebraic $k$-group $G$. Under what conditions can I assume that a connected nonsingular affi …
- 3,637