All Questions
Tagged with localization ag.algebraic-geometry
9 questions with no upvoted or accepted answers
7
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0
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Ample divisors on $T$-varieties
Question: how does one use a torus action to help decide whether a divisor or line bundle is ample?
In more detail: I have a (normal, but usually rather singular) $T$-variety $X$, where $T$ is an ...
- 6,162
7
votes
0
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376
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Grothendieck Riemann Roch is abelian localisation on loop spaces
Abelian localisation says approximately that for a proper equivaraint map $f:X\to Y$ between schemes with a $\mathbf{G}_m$ action, the pushforward on cohomology $f_*\omega$ can be computed by the ...
- 5,711
6
votes
0
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371
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Geometric meaning of localization at $(1+I)$?
Let $I\vartriangleleft A$ be an ideal of a commutative ring. Consider the submonoid $1+I\subset A$. What is the geometric interpretation of localization at this submonoid? How does it relate to the ...
- 10.5k
6
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180
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Abelian localisation for K theory?
Let $X$ be a scheme acted upon by $\mathbf{G}_m$ and $K(X)=K_0(\text{Perf}X)$ the Thomason-Trobaugh K theory. Is there a localisation theorem in this context? By this I mean something like
$$\text{id}...
- 5,711
3
votes
0
answers
343
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Localization of the pushforward in equivariant cohomology
I am reading Nekrasov's paper and in page 2 he considers the $G \times T^2$ equivariant cohomology of the (compactified) moduli space $\tilde{M_k}$ of $U(N)$ instantons on $\mathbb{C}^2$. Here $G$ ...
- 587
2
votes
0
answers
60
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When localization commutes with arbitrary intersection of ideals
For a commutative ring with identity we know that in general localization does not commute with arbitrary intersection of ideals. I am looking for a paper that considers equivalent condition(s) for ...
- 21
2
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0
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136
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Some relative GW calculations
I have a question about the $\psi$ class in the following paper of Graber and Vakil:
https://arxiv.org/abs/math/0309227
For $k,d\geq 2$, and a partition $d=d_1+\cdots+d_k$ of $d$ into positive ...
1
vote
0
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125
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Different ways to construct the isogeny category of abelian varieties
Let $k$ be a field and let $\mathbf{AV}_{/k}$ be the category of abelian varieties over $k$. I'm interested in different definitions of the isogeny category of $\mathbf{AV}_{/k}$.
Of course, the ...
- 804
1
vote
0
answers
172
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Local cohomology commuting with fiber
Let $A$ be a nice commutative ring (say, $A=k[t_1,\ldots , t_n]$, ring of polynomials over an algebraically closed field $k$).
Let $M$ be an $A[x]$-module, which is finitely generated as an $A$-...
- 5,562