All Questions
Tagged with ag.algebraic-geometry kt.k-theory-and-homology
58 questions with no upvoted or accepted answers
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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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Two questions on canonical line bundle over $\mathbb{C}P^{n}$
The canonical line bundle over $\mathbb{C}P^{n}$ is denoted by $\ell_{n}$. It is well known that: $$(\ell_{1}\otimes \ell_{1})\oplus1 \simeq\ell_{1}\oplus\ell_{1}$$ Both sides are isomorphic ...
- 356
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Relative Gersten resolution for a flat projective morphism
I am reading two papers by Daniel Grayson: "Localization for flat modules in algebraic K-theory" and "Algebraic cycles and algebraic K-theory" and I am wondering if any recent advances in K-theory ...
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The right (not the left 'Suslin complex' one) adjoint to the embedding of $ DM^{eff} $ into $D(ShvTr) $?
Inside the derived category of Nisnevich sheaves with transfers there is the category $DM^{eff} $ of Voevodsky's effective motivic complexes (actually, Voevodsky only considered bounded above ...
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Special properties of (the $\gamma$-filtration of) $K$-theory of affine varieties.
Let $A$ be a smooth affine variety of dimension $n$. Are there any facts known on $K_{\ast}(A)$ and its $\gamma$-filtration which do not hold for $K_*(V)$ for an arbitrary smooth $V$ (of the same ...
- 16.9k
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When the class of a complex is necessarily equi-dimensional
Let $P$ be a smooth projective variety. For an object $X$ of $D_{perf}(P)$ (i.e. a bounded perfect complex of $\mathfrak{O}_P$-module sheaves) we consider its class $[X]$ in $K_0(P)\otimes \mathbb{Q}(\...
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Projectivity of equivariant K-theory of toric variety
I'm looking at Vezzosi and Vistoli's paper: Higher algebraic K-theory for actions of diagonalizable groups.
In Theorem 6.9, they prove that the $T$-equivariant K-theory of a smooth projective toric ...
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Surjectivity of the Albanese map of the moduli space of stable vector bundles
I have a naive question:(I saw that it is related to relative K-theory of Hodge-Deligne and also Nadel-Chern-Weil theory )
Let $\mathcal M (r, d)$ be the moduli space of stable vector bundles of rank ...
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