User quetzalcube - MathOverflow

Reference for Cech cohomology for Nisnevich topology

2013-05-15T10:06:32Z

I need the theorems that prove that Nisnevich cohomology can be computed by the Cech complex similar to what happens in the étale topology.

I know this has to be true since (Morel-Voevodsky: $\mathbb{A}^1$-homotopy theory of schemes. Publ. Math. IHES (1999)) say it at the beggining of sectio 3, page 95... but they don't give the reference!

Thank you very much for your help!

Why are Kan fibrations and Serre fibrations so important?

2012-03-15T17:23:34Z

I know so far that Kan fibrations are the abstract analog of Serre fibrations but i don't have any expierience with neither one of them so

Could someone give a motivation why Kan fibrations (or if easier, Serre fibrations) are so important in homotopy theory of simplicial sets?

Thank you

Alexander duality theorem for CW-complexes and stable homotopy theory

2011-10-17T07:40:31Z

In Adams, J.F. Infinite Loop Spaces Princ. Univ. Press. page 9 he states Alexander duality theorem

Theorem:[Alexander Duality] $$ H^r(X,G)=H_{n-r+1}(S^n-X,G)$$

for finite CW-complexes with a "nice embedding". That is to say, $S^n-X$ has a CW-complex $Y$ as deformation retract and $X$ is a deformation retract of $S^n-Y$.

My first question is the following: Do you know if every CW-complex admits a nice embedding into some $S^n$? if so, could you give a reference?

Thanks in advance.

Reference: Learning noncommutative geometry and C^* algebras

2011-02-03T11:27:41Z

I am starting to study noncommutative geometry and C^* algebras so my question is

Does anyone knows a good reference on this subject?

I would like a basic book with intuitions for definitions and this kind of things. I come from algebraic geometry so if it talks a bit about the relation with it would be highly appreciated.

I have already taken a look to Conne's book but I find it too hard and I'm currently studying Landi's but it lacks lots of proofs (he refers to several papers)

Thanks in advance

Are finite correspondances flat?

2011-01-13T19:04:21Z

In Voevodsky&Mazza&Weibel's book on motivic cohomology they define "an elementary correspondance from X (Smooth connected scheme over $k$) to Y (separated scheme over $k$) as an irreducible closed subset $W$ of $X\times Y$ whose associated integral subscheme is finite and surjective over $X$."

As far as I know $W$ would be flat over $X$ if it was Cohen-Macaulay so...

1.- ¿Is $W$ flat over $X$?

If not,

2.- why isn't this a common sense assumption? Could anyone give an example of why nonflat elementary correspondaces should be allowed?

Thanks in advance

Comment by Quetzalcube

2013-05-17T07:49:59Z

Oups, you are right. Thank you very much. Prop. 3.1.9 is actually what i was looking for. Sorry for my mistake!

Comment by Quetzalcube

2011-06-14T14:15:13Z

$v$ is the normal bundle sorry ( i don't how to érase the comment) but still: what is $w_i$? thanks

Comment by Quetzalcube

2011-06-14T14:10:09Z

please, could you define what is $w_i$ and $v$ in the formula $Sq^i(x)=f_*(w_i(v))$? Thanks a lot in advance