fpqc

Hi guys, I have a quick question about the homotopy category. Let $\mathcal{A}$ be any abelian category and let $A^{\bullet}, B^{\bullet}, C^{\bullet}$ be any three complexes. Then do we have a Tensor-Hom adjunction $Hom(Tot(A^{\bullet} \otimes B^{\bullet}), C^{\bullet}) = Hom(A^{\bullet}, Hom^{\bullet}(B^{\bullet} \otimes C^{\bullet}))$?

it's a very useful procedure to know

It's the only one I really care about

@BalarkaSen The only real blow up calculation I've done is the one in Deligne-Mumford :)

see ya

I'm going to answer a math.se question on the blow up

alright guys

Yeah they want the reputation

we're forced to go to MO

It crowds out people like me

yeah

Used to be a lot of high quality stuff

@TedShifrin I think the quality of math.se has really gone down honestly

@TedShifrin it was his undergrad thesis

hrinking tubes and variants of the Gauss-Bonnet formula

you probably know andrasz vasy too

damn man

ahhhh

@BalarkaSen Yes. I'm in AG but also in the arithmetic things too.

@TedShifrin Wait wasn't rafe a student of melrose?

@TedShifrin Really? Rafe taught the second course in the grad analysis sequence

I work in algebraic geometry.

@TedShifrin No. We met here!

@BalarkaSen math.stanford.edu/~conrad/Weil2seminar/Notes/L19.pdf

My talk on was on april 12th

@BalarkaSen At some point there's various annoying commutative diagrams that one has to check are true. And no one knows except Brian, de Jong and Gabber

@TedShifrin Hello!

The proof of Grothendieck-Lefschetz is a long devissage using poincare duality, etc

This was this year's seminar on etale cohomology

@BalarkaSen math.stanford.edu/~conrad/Weil2seminar

@BalarkaSen The problem with learning etale cohomolgoy is that you need to know algebraic geometry. The proofs are often quite complicated and involve a lot of devissage

@BalarkaSen We would be able to prove the functional equation and rationality of zeta

Basically Andre Weil realized that if we could have a "Weil Cohomology Theory", i.e. something that behaves like singular cohomology for varieties over a finite field

@BalarkaSen If you care about topology, maybe you'll care about \'{e}tale cohomology.

@BalarkaSen Even in number theory too.

@BalarkaSen Sure.

@BalarkaSen Of course in other fields too there are many great achievements

@BalarkaSen I think it's on of the triumphs of 20th century math, along with say the proof of the weil conjectures and fermat's last theorem

g

I mean surely you care about the moduli space of riemann surfaces of genus

Depends on what you read though

It's very stacky

Yes.

@BalarkaSen Yeah I work in moduli theory.

@BalarkaSen which uni?

Now write it as (1+1/n)/ (1/n) and use lh

you have to prove the limit of (1+1/n)^n is 1.

Look, take the log of that

It's just e man

your question is what is $\lim (1 + 1/n)^n$?