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This tag is used if a reference is needed in a paper or textbook on a specific result.

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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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"
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar