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Results tagged with ag.algebraic-geometry
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user 17218
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
1
vote
1
answer
209
views
Zariski closure of the boundary of a closed convex subset of ${\mathbb R}^n$
Let $\eta$ be a closed convex subset of ${\mathbb R}^n$ of convex dimension $n$ (not necessarily compact) with nonempty boundary $\partial \eta$. Then $\eta$ is an $n$-dimensional topological manifol …
- 4,985
12
votes
1
answer
1k
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A problem in commutative algebra whose solution requires algebraic geometry (resp., noncommu...
One can argue that commutative algebra is affine algebraic geometry. However, a great deal of commutative algebra generalizes to non-commutative algebra, and in that setting there is little geometry, …
- 4,985
1
vote
A relation between annihilators and ideals
A semiprime operation on a ring $R$ (commutative with identity) is a closure operation $c: I \longmapsto I^c$ on the lattice of all ideals of $R$ such that $I^c J^c \subseteq (IJ)^c$ for all ideals $I …
- 4,985
12
votes
Accepted
Some questions about the ring Z((x))
Question 1: The fraction field is the same as that of $\mathbb{Z}[[x]]$. It can be gotten by inverting all irreducibles. The irreducibles of the UFD $\mathbb{Z}[[x]]$ are described in Theorem 1.4 of …
- 4,985
5
votes
Algebraic theorems with no known algebraic proofs
Dirichlet's theorem on primes in arithmetic progression: if $a$ and $b$ are any relatively prime positive integers, then there are infinitely many prime numbers of the form $a+nb$ for positive integer …