All Questions
Tagged with motives kt.k-theory-and-homology
8 questions with no upvoted or accepted answers
10
votes
0
answers
340
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Geometric vs combinatorial motives over Spec Z
Consider the category of reduced schemes of finite type over $\mathbb{Z}$. Take the Grothendieck group of this category, i.e. the free abelian group on isomorphism classes, modulo the usual "syzygy" ...
- 5,637
9
votes
0
answers
463
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Beilinson regulators and Bloch's mythological algebraic intermediate Jacobians
In the paper introducing his motivic cycle complexes, Bloch outlines a project he says he was going to return to in the future:
Towards the end of page 270, he says, given a smooth projective variety ...
user95222
6
votes
0
answers
242
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Are Tate twists of t-positive motives positive with respect to the Voevodsky's homotopy t-structure?
Let $X$ be a Voevodsky's motif (over a perfect field) that belongs to the positive part of the homotopy $t$-structure (i.e. its cohomology as an object of $D^-(ShSmCor)$ is zero in negative degrees). ...
- 16.9k
4
votes
0
answers
426
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In which "sense" unramified Milnor-Witt K-groups are unramified
Let $X$ be an integral locally noetherian smooth
scheme over base field $k$. Then for every $x \in X^{(1)}$ point of codimension $1$, the stalk $\mathcal{O}_{X,x}$ is a discrete valuation
ring. ...
- 6,018
4
votes
0
answers
205
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$\mathbf{A}^1$- contractibility
Suppose $U$ is an $\mathbf{A}^1$-contractible smooth scheme over a field $k$, that is, it is isomorphic to a point in the $\mathbf{A}^1$-homotopy category of smooth schemes over $k$.
Does motivic ...
user119470
4
votes
0
answers
218
views
The 'most general' papers on rational Borel-Moore motivic homology and K'-theory?
There are two ways to define Borel-Moore motivic homology (of schemes) with rational coefficients: one should either consider certain complexes of algebraic cycles, or the $\gamma$-filtrations of ...
- 16.9k
4
votes
0
answers
197
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The vanishing of homotopy invariant $K$-theory of dg-categories
In my previous question The vanishing of non-connective K-theory in negative degrees
I asked when one can be sure that the negative non-connective $K$-groups of a differential graded category vanish. ...
- 16.9k
1
vote
0
answers
140
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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 ...
- 16.9k