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Results tagged with reference-request
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user 4008
This tag is used if a reference is needed in a paper or textbook on a specific result.
21
votes
Accepted
Chevalley–Shephard–Todd theorem
There are indeed many presentations (if I remember correctly Bourbaki has it)
but the proof is very elegant and short so that I find it hard to refrain from giving
it. Let $H$ be the normal subgroup o …
- 22.6k
16
votes
Accepted
Where can I easily look up / calculate (abelian) group cohomology?
This group is best understood in terms of the universal coefficient formula,
i.e., in terms of the homology of the involved group. Hence, if $A$ is any
abelian group we have $H_1(A)=A$ and the additio …
- 22.6k
15
votes
Accepted
Is a polynomial group law on $\mathbb{R}^n$ automatically nilpotent?
This is true and is in "Michel Lazard: Sur la nilpotence de certains groupes algébriques, Comptes Rendus, vol 241, 1955, 1687--1689"
- 22.6k
15
votes
Accepted
$Sq^1$ cohomology of spaces
I think the easiest way to understand the Bockstein spectral sequence is through the exact couple coming from the long exact sequence of cohomology associated to $0\to\mathbb Z\to\mathbb Z\to \mathbb …
- 22.6k
12
votes
What is the etymology of the term "perverse sheaf"?
One explanation I heard (it may have been from MacPherson but I am not sure) was that "perverse" was used in the sense of "contrary", the cycles used in the definition refuse to move away from the sin …
- 22.6k
12
votes
Accepted
Is the functor of divided powers a weakly monoidal functor?
This is a well-known result and, apart from terminology, should be found in
Roby, Norbert
Lois polynômes multiplicatives universelles. (French. English summary)
C. R. Acad. Sci. Paris Sér. A-B 290 (19 …
- 22.6k
8
votes
Accepted
Liftability of Enriques Surfaces (from char. p to zero)
This may not be exactly the answer you are looking for: I and Nick
Shepherd-Barron have an unpublished (so far) proof of liftability in
characteristic $2$, the only non-trivial case. To atone for the …
- 22.6k
6
votes
Accepted
How to show that a form of Euler characteristic is constant for a family of schemes?
Define $\chi(\mathcal M,\mathcal N)$ for all finite length $\mathcal O_X$-modules. It is additive in both arguments so for its computation we get
$$
\chi(\mathcal M,\mathcal N) = \sum_{x,y}
\mathrm{lg …
- 22.6k
2
votes
Simplicity of (complex) orthogonal groups
A reference with a small amount of patching to do is Bourbakie: Groupes et algèbres de Lie, Chap IV, 2.7, it uses the theory of BN-pairs (which there are called Tits systems). It is shows that the onl …
- 22.6k
2
votes
Non-vanishing cohomology of line bundles on projective varieties in prime characteristic?
I am not sure to which extent your questions are really related to positive
characteristic.
The obvious difference between positive characteristic and characteristic zero
related to the question is o …
- 22.6k