All Questions
Tagged with chow-groups algebraic-k-theory
7 questions
1
vote
1
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217
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Meaning of torsion points in a Roitman's theorem
I am having some problems to understand the meaning of the following theorem due to Roitmann. I found this theorem in Voisin's book: Hodge Theory and Complex Algebraic Geometry, Volume II, page ...
- 519
0
votes
0
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172
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Pullback of algebraic $K$-theory along the surjection of abelian varieties
Given a surjective homomorphism of abelian varieties $f:A\rightarrow B$ where $\text{dim}(A)>\text{dim}(B)$, does $f^*$ induce a rational injection of algebraic $K$-theory? According to the ...
- 5,901
2
votes
0
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331
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Few questions about the algebraic cycles and the conjectures of Beilinson and Tate
I have three slightly related questions about algebraic cycles which I am just going to list them. I'd really appreciate any answers:
1) Is there any example of a smooth projective variety $X$ over a ...
- 5,901
7
votes
1
answer
474
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Motivic $\mathbf{Z}(1)$
I know that the Bloch higher Chow complex, $\mathbf{Z}(i)_{\mathcal{M}}$, on a smooth scheme over a field $k$, reads, in degree $1$:
$$\mathbf{Z}(1)_{\mathcal{M}}\simeq\mathbf{G}_m[-1].$$
How to see ...
user113393
9
votes
0
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632
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Relative Chow groups
Most cohomologies have the notion of cohomology with support on a closed subspace, and also cohomology with compact support. In general, for any morphism $f\colon Y\to Z$ the inverse image fits into a ...
- 2,871
9
votes
0
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1k
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Motivic cohomology of a point
I was wondering how much is known about the integral motivic cohomology groups of $\mathrm{Spec}\, k$, $H^{n,p}_{\mathrm{mot}}(\mathrm{Spec}\, k,\mathbb{Z})$. One knows that $H^{n,n}_{\mathrm{mot}}(\...
- 596
4
votes
2
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491
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on the Zariski sheafification of Quillen's K-theory
Let $X$ be a smooth k-variety and denote by $K_n$ Quillen's K-theory sheaf, that is: the Zariski sheaf on $X$ associated to the presheaf $U \mapsto K_n(U)$.
The Bloch-Quillen formula says that $CH^n(...
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