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13
votes
1
answer
559
views
Intersection of subvarieties versus ranks of Chow groups modulo numerical equivalences
A nice property of $\mathbb P^n$ is:
Property 1: Two subvarieties $U,V$ such that $\operatorname{dim} U +\operatorname{dim} V \geq n$ always intersect.
(for example, any 2 curves in $\mathbb P^2 …
12
votes
2
answers
648
views
Maps between K-groups induced by rings homomorphism
Let $f: R\to S$ be a map between two commutative Noetherian rings. Let $G_0(R)=K_0(mod R)$ be the Grothendieck group of finite generated modules over $R$. It means $G_0(R)$ is the quotient of the free …
11
votes
2
answers
676
views
Genus of smooth varieties with small Chow group
Let $X$ be a smooth projective variety over $\mathbb C$ with $d = \dim X \geq 1$. Let $CH(X)$ denotes the total Chow group of (cycles modulo rational equivalences of) $X$ and $CH(X)_{\mathbb Q} = CH( …
8
votes
Accepted
Isolated hypersurface singularities, Chow groups and D-branes
Assume $k= \mathbf C$ and $W$ homogeneous. Let $X=Proj (k[x_1,\cdots,x_n]/(W))$. $X$ is then a smooth hypersuraface in $\mathbb P_{n-1}$.
Assume $n=2d$ is even. Corollary 3.10 of the paper you quote …
6
votes
1
answer
999
views
Seeking examples or proof: injectivity of Cartan homomorphism for commutative rings?
This question is motivated by some issue raised by David Speyer in this question.
Let $R$ be a ring. Let $K_0(R)$ and $G_0(R)$ be the Grothendieck groups of f.g. projective modules and f.g. modules …
3
votes
The localisation long exact sequence in K-theory over an arbitrary base
I do not have the reference with me right now, but I think the localization sequence for K-theory over general base was handled in:
R. W. Thomason, T. Trobaugh, Higher algebraic K-theory of schemes
…