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2d
revised Families of abelian varieties on the line (or more generally simply connected varieties)
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2d
answered Families of abelian varieties on the line (or more generally simply connected varieties)
2d
comment How many real-analytic forms exist on a real-analytic manifold?
Definitely, it would be infinite dim in general. Take $M=S^1=\mathbb{R}/2\pi \mathbb{Z}$, then consider $\{\sin (nx) dx\}$.
Apr
26
comment Euler characteristic - reference question
Never mind, it's too early in the morning here.
Apr
26
comment Euler characteristic - reference question
Surely you want some additional hypotheses, after all $\mathcal F=0$ is constructible.
Apr
16
answered Confusion surrounding the Koszul-Malgrange theorem
Apr
13
comment Spin structures on schemes
If I remember correctly (it's been a while) the usual condition for existence is of a spin structure on a manifold is for $w_2=0$. So for a complex manifold, it would be enough to know that $c_1$ is even, or that the canoncal bundle has a square root. These are classically called theta characteristics. This is probably different from what you are after, but I thought I'd mention it.
Apr
11
comment Is $(\mathbb R^d/\mathbb Z^d,+)$, $d>2$, isomorphic to some group of an algebraic surface?
An abelian variety is a smooth projective variety with a group law compatible with the variety structure. Over $\mathbb{C}$, it is necessarily a torus. It is hard to say much more in comment box, but sounds like this is what you want.
Apr
11
comment Is $(\mathbb R^d/\mathbb Z^d,+)$, $d>2$, isomorphic to some group of an algebraic surface?
Yes, these are called abelian varieties. If you search, you will find a lot of material on this topic.
Apr
9
answered Resolution of singularities in étale cohomology
Apr
6
answered Intuition behind the definition of finite correspondences
Apr
4
answered Relationship between $ \mathcal{D} $ - modules, Tannakian formalism and Galois theory of monodromy representations
Apr
4
comment Is the category of mixed Hodge modules bi-filtered?
Oh yea good point. So no, in either case.
Apr
4
comment Is the category of mixed Hodge modules bi-filtered?
Maybe yes, maybe no. No using Saito's original definition, because $F$ is almost never defined over $\mathbb{Q}$. On the other hand, Sabbah and Schnell have been reworking the foundations, so that it is no longer necessary to have a $\mathbb{Q}$ "lattice" in their version. See cmls.polytechnique.fr/perso/sabbah.claude/MHMProject/mhm.html
Feb
29
answered Reference for Nori motives
Feb
28
comment Étale coverings of cubics and gluings
Abstractly $\tilde X$ is the affine line. There is an automorphism which interchanges any two points, so in particular $x_1, x_2$. So you should get the same covering up to isomorphism.
Feb
25
comment Varieties with only top $\ell$-adic cohomology not vanish?
David, yes, I think it's doable also. After spreading the variety out over a finitely generated ring, you can use the comparison theorem + proper base change.
Feb
21
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Feb
17
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Feb
16
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