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Results tagged with kt.k-theory-and-homology
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user 2503
Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
3
votes
Does a fully faithful functor between triangulated categories induce embedding of their Grot...
One should really only talk about $K_0$ of small categories, otherwise one runs into the difficulty explained in Matthias's comment. Assuming $\mathcal{B}$ is small, let me identify $\mathcal{A}$ wit …
- 5,901
8
votes
Accepted
Could we extend the exact sequence $K^0(X)\to K_0(X)\to K_0(D_{sg}(X))\to 0$ to the left?
The exact sequence of triangulated categories
$$ Perf(X)\to D^b_{coh}(X)\to D_{sg}(X) $$
may be lifted to an exact sequence of stable $\infty$-categories or dg-categories in the sense of BGT: choose …
- 5,901
9
votes
Accepted
K theory long exact sequence
Regarding the first question:
If $X$ is quasi-compact quasi-separated and $U \to X$ is a quasi-compact open immersion, then Thomason-Trobaugh showed that there is a "proto-localization sequence", i.e …
- 5,901