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12h

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Commuting diagram, algebraic cycles and Ktheory
$ch(A\boxtimes B) = ch(p^*A\otimes q^*B)= p^*ch(A)\cdot q^*ch(B) = ch(A)\times ch(B)$, where $p,q$ denote projections on $X\times Y$, and I'm using naturality and the fact that $ch$ is homomorphism (unless that was your question). 
Aug
23 
revised 
Vanishing of sheaf cohomology with compact support
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Aug
22 
revised 
Vanishing of sheaf cohomology with compact support
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Aug
22 
comment 
Vanishing of sheaf cohomology with compact support
Igor, thanks. I'll edit. 
Aug
22 
answered  Vanishing of sheaf cohomology with compact support 
Aug
15 
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Motivic fundamental group of the moduli space of curves?
Will, no I would agree that these examples aren't exotic. The pure graded part of the moduli of semistable bundles come from $Sp_{2g}$ as you surmised. 
Aug
14 
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Motivic fundamental group of the moduli space of curves?
Actually, I think that the reductive part of $\pi_1^{mot}(M_g)$ would bigger than $Sp_{2g}$. You can see my answer to mathoverflow.net/questions/186133/… for why I think so. 
Aug
12 
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nonsingular schemes and regularity of stalks
I didn't down vote you, but I do have to ask, what is your definition of nonsingular? Often nonsingular=regular by definition. 
Aug
7 
answered  When $mB \neq B$? $m$ is a maximal ideal of $A$, $A \subseteq B$ 
Jul
29 
awarded  Good Answer 
Jul
29 
comment 
Genus of a plane curve of the form $\prod_{i=1}^n (a_iX+b_iY+Z) = Z^n$
It depends on whether genus means arithmetic or geometric genus. Of course, you and probably the OP mean the latter. 
Jul
28 
awarded  Nice Answer 
Jul
27 
awarded  Nice Answer 
Jul
26 
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Relationship between étale and topological $K(\pi,1)$s
Yes, I believe 2 and 3 are still open. Serre, in one of his books, asked explicitly whether the Higman group occurs as the fundamental group of a smooth projective variety. If so, it would provide a counterexample to 2. I'm not aware of any progress on this. 
Jul
26 
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Relationship between étale and topological $K(\pi,1)$s
It's kind of a shame that the name "good group" seems to have stuck. Given the large community of mathematicians here, I wonder if can vote to change it to something more else. How about "Serre group"? 
Jul
26 
revised 
Relationship between étale and topological $K(\pi,1)$s
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Jul
26 
comment 
Relationship between étale and topological $K(\pi,1)$s
The point of going to level $\ge 3$ is that $\Gamma(n)$ acts without fixed points, so you can use the usual $\pi_1$. 
Jul
25 
answered  Relationship between étale and topological $K(\pi,1)$s 
Jul
25 
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Relationship between étale and topological $K(\pi,1)$s
I strongly suspect that the main question is false, but I'll need to think more about it. There is a typo in 2 by the way. 2 and 3 are open as far as I know. Although there exists smooth projective varieties with non residually finite fundamental groups (Toledo,...). 
Jul
24 
revised 
Intuition behind the Kodaira Vanishing Theorem?
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