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I'm having trouble finding a reference for something that I think should be in the literature. Consider a short exact sequence of bounded double-complexes, in an abelian category: $$0 \rightarrow A^{ …

I think that the best reference for the infinitesimal site, especially if one is motivated to learn crystalline cohomology, is found in Grothendieck's lectures "Crystals and the De Rham Cohomology of …

One of the most important applications of etale cohomology is to Deligne-Lusztig theory, and the large subsequent body of work approaching the representation of finite groups of Lie type using $\ell$- …

One reference: The section "The algebraic fundamental group of a reductive group", in "Abelian Galois Cohomology of Reductive Groups", by Mikhail Borovoi. This has exactly what you're looking for, I …

If you are looking for an online reference, you can check out Brian Conrads course notes on differential geometry. Near the bottom of that page, you can find the handout with Stokes theorem for manif …

I agree with some of the comments that "profinite set" is not a standard term. But you can certainly look at the category of pro-(finite sets). In other words, begin with the category $Set_f$ of fin …

I'd recommend first that you and your friend spend more time with Tits :), "Reductive groups over local fields", from the Corvallis volume (free online, last time I checked). Undoubtably there are ot …

Consider a finite-rank free $Z$-module $Y$. Let $c: Y \times Y \rightarrow Z$ be a $Z$-bilinear form. Assume that $c(y_1, y_2) + c(y_2, y_1)$ is even, for all $y_1, y_2 \in $. Then $c$ "incarnates …

I think, although it's dated later than Deligne's paper that you mentioned, that the first written instance of Kazhdan's principle is in the paper "Representations of groups over close local fields", …

An undergraduate is performing some computations, related to a Sato-Tate conjecture of $U(3)$ type (a curve over $Q$, for which the roots of local L-functions look like eigenvalues of a random matrix …

Let $G$ be a connected reductive group over a (perfect, why not) field $F$. Let $m$, $pr_1$, $pr_2$ denote the multiplication, first, and second projection maps from $G \times G$ to $G$. Then I'm pr …

Let $F$ be a local nonarchimedean field. Let $n$ be a positive integer for which the group $\mu_n(F)$ of $n^{th}$ roots of unity in $F$ has order $n$. Let $\epsilon: \mu_n(F) \rightarrow C^\times$ b …

When I was a graduate student, a professor (who will remain nameless since I might be misquoting) said something along the lines of "If you want to see where the errors in a math paper are, just look …

I am looking for a reference for the following facts in functional analysis and topology. (If these "facts" are not true, I suppose I'm looking for the closest approximation which is true.) Let $X$ …

One suggestion: "Period mappings and Period Domains", by Carlson, Muller-Stach, and Peters, in the Cambridge studies in advanced mathematics series. It's a very nice read, and each chapter comes wit …