All Questions
9 questions with no upvoted or accepted answers
9
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Some questions about Clausen's third IHES lecture on Efimov K-theory
I have some questions about the last theorem stated by Clausen at https://youtu.be/2xNG4rHUC6U?si=yw9eYiygLegH0nQK&t=4319. I'm not very familar with the definitions, so please correct me about any ...
- 2,356
8
votes
0
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440
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Poincaré duality for topological $K$-theory
Let $n$ be an even number. Let $X$ be a $n$-dimensional complex projective manifold with
$H^{2m+1}(X,\mathbb{Z})=0$, for all $0\leq m\leq n-1$.
$H^{2m}(X,\mathbb{Z})$ is a free $\mathbb{Z}$-module ...
user39380
6
votes
0
answers
137
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Comparison of K-groups of (affine) singular schemes with K'=G-groups
It is well known that Quillen K-theory coincides with $K'=G$-theory for regular schemes, and can be distinct from it for singular ones. Are there any methods for studying this distinctions? In ...
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4
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0
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324
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The restriction of the Gersten resolution (for etale cohomology) onto a closed subvariety.
There is a very important result of Bloch and Ogus: for any smooth variety $X$ and fixed $r\in \mathbb{Z}$, $r\ge 0$, $l$ is prime to the residue field characteristic, the Zariski sheafification of ...
- 16.9k
2
votes
0
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129
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Flag variety type Beilinson resolution
The Beilinson resolution is a locally free sheaves resolution for sheaf $\Delta_*\mathcal{O}_{\mathbb{P}}$,where $\Delta: \mathbb{P}\to \mathbb{P}\times\mathbb{P}$ is the diagonal embedding of ...
- 653
2
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0
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181
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Is there a degeneration formula for Gromov-Witten K-theoretic invariants?
By Gromov-Witten K-theoretic invariants (call them KGW) I mean the invariants defined by Givental and Lee.
I expect the formula expresses the KGW of the generic fiber of a given degeneration in terms ...
- 21
2
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0
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194
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Varieties with Chow groups supported in positive codimension: examples and properties?
In their 1983 paper "Remarks on correspondences and algebraic cycles" Bloch and Srinivas proved several interesting properties of smooth proper varieties (over universal domains) whose Chow groups of ...
- 16.9k
1
vote
0
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68
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Metric and connection on virtual bundles
Let $E=[E^+]-[E^-]$ be an element of the Grothendieck group $K(X)$ of a compact Kahler manifold $X$.
Does it exist a way to define more "geometric" structures on $E\in K(X)$ such that a ...
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1
vote
0
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203
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Is there any computation of $K^0(X)$ and $K_0(X)$ for a singular curve $X$?
Let $X$ be a projective curve over an algebraic closed field $k$ which characteristic zero. Define $K^0(X)$ as the Grothendieck group of the derived category $Perf(X)$ and $K_0(X)$ as the Grothendieck ...
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