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awarded  Nice Answer
Mar
16
comment Mixed Hodge structure and cup product
I had similar thoughts. I wonder how many people who voted to close knew the answer. (Test: Is the category of mixed Hodge structures Tannakian, true of false?)
Mar
14
comment Reference Request: Fundamental Group Scheme
I agree that the question seems reasonable and doesn't deserve to be closed. However, my suggestion to Priyankur would be to learn a bit more algebraic geometry before jumping into this topic. At the very least, first learn a bit about the etale fundamental group from Murre's "Lectures on Grothendieck's fundamental group" TIFR.
Mar
9
comment Terminology regarding divisor on a curve
The "support of $D$" sounds good to me.
Feb
26
comment Is there an analogue of the Tate (and Hodge) conjecture for varieties that are not proper smooth (i.e., the mixed case)?
If $X$ is smooth at least, you can use duality to flip to a cohomological statement. Then it would a special case. This is actually what I meant by my somewhat cryptic comment "expected to hold for $i=2p$ (Hodge/Tate)"
Feb
25
comment Is there an analogue of the Tate (and Hodge) conjecture for varieties that are not proper smooth (i.e., the mixed case)?
Yes. A triangulated category is all you need for the $Ext$'s.
Feb
25
revised Is there an analogue of the Tate (and Hodge) conjecture for varieties that are not proper smooth (i.e., the mixed case)?
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Feb
25
comment Is there an analogue of the Tate (and Hodge) conjecture for varieties that are not proper smooth (i.e., the mixed case)?
OK, I'll try to expand this a bit later when I have more time.
Feb
25
answered Is there an analogue of the Tate (and Hodge) conjecture for varieties that are not proper smooth (i.e., the mixed case)?
Feb
23
answered Proof of “generic curve of genus at least 2 has no nontrivial maps to a positive genus curve”
Feb
23
comment Proof of “generic curve of genus at least 2 has no nontrivial maps to a positive genus curve”
For your first question, it follows from from Cor. 17.5.2 of Birkenhake and Lange's book on Complex Abelian Varieties (2nd ed), but I'm sure there are more suitable references.
Feb
23
comment Proof of “generic curve of genus at least 2 has no nontrivial maps to a positive genus curve”
Of course, Jason is correct. However, a very general point of $M_g$ (by which I mean, exclude a countable union of proper sub varieties) corresponds to a curve with a simple Jacobian. This curve can't map onto anything of smaller genus. (This is over $\mathbb{C}$.)
Feb
21
awarded  Yearling
Feb
18
answered Hodge structure of relative cohomology groups
Jan
29
comment de Rham cohomology of smooth affine varieties
Not really, but this is not a bad thing. I added some further comments.
Jan
29
revised de Rham cohomology of smooth affine varieties
added 578 characters in body
Jan
29
answered de Rham cohomology of smooth affine varieties
Jan
19
answered periods of Mixed Hodge Structures
Jan
13
awarded  Nice Answer