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Feb
5
revised Obstructed automorphisms of schemes
added 360 characters in body
Feb
5
answered Obstructed automorphisms of schemes
Feb
5
comment Distinguished triangle and short exact sequence
While this may not be difficult for an expert, it strikes me as pretty reasonable graduate student level question. Or have our standards gotten that high?
Jan
26
comment some terminologies on limiting mixed hodge structures or rather Derived categories
Hi Feng, I agree that talking about exact sequences in this context doesn't make sense, but I think that Steenbrink meant that these sequences can be realized by exact sequences of complexes. Try to take a look at discussion of limit MHS in the book by Peters and Steenbrink, and see if that clears anything up.
Jan
25
revised A conjecture of Cheeger about intersection cohomology and $L^2$- cohomology
added 47 characters in body
Jan
24
awarded  Revival
Jan
24
revised A conjecture of Cheeger about intersection cohomology and $L^2$- cohomology
added 303 characters in body
Jan
24
answered A conjecture of Cheeger about intersection cohomology and $L^2$- cohomology
Jan
13
comment History of the functor of points
Surely, it was due to Grothendieck, but well before 1973. One can find functors of points for schemes (originally called preschemes) discussed in EGA I (chap I, sect 3.4), which was written in 1960.
Jan
1
awarded  Nice Answer
Dec
22
comment Kahlerness of the projectivized cotangent bundle
Call your space $P$. It has a projection $\pi:P\to X$. It's a projective space bundle. So $P$ has a positive semidefinite $(1,1)$-form $\phi$ which restricts to the Fubini-Study form on the fibres (I'll let you check). Now consider $\phi+\pi^*\omega$, where $\omega$ is the Kahler form on $X$...
Dec
4
revised Is there a description of variation of (mixed) Hodge Structures in terms of a Deligne operator?
added 499 characters in body
Nov
30
answered Is there a description of variation of (mixed) Hodge Structures in terms of a Deligne operator?
Nov
8
comment Is every complex rational algebraic variety simply connected for the Euclidean topology?
It's also false for singular rational varieties (e.g. for a nodal cubic). In the positive direction: a nonsingular rational projective variety is simply connected.
Nov
2
comment A specific linear differential equation on $\mathbb{C}-\{0,1\}$ whose monodromy group represents the fundamental group of $\mathbb{C}-\{0,1\}$
You can use a hypergeometric equation. This is has three regular singular points including $\infty$.
Nov
2
comment the normalized blowup
Consider $0\to f_* \to f_*\mathcal{O}_{Y^\nu}=\mathcal{O}_X\to f_*\mathcal{O}/I$. The right hand sheaf is coherent and supported at $x$. This would be enough to conclude $I$ is $m_x$ primary.
Oct
14
awarded  Nice Answer
Oct
12
revised Why should curves be two-dimensional?
added 183 characters in body
Oct
12
answered Why should curves be two-dimensional?
Oct
9
revised Algebraic proof without using comparison theorem for étale cohomology
added 63 characters in body