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I have a very simple proof; yet I am affraid something is wrong with it. So, for each hypercover of $X$ the (co)homologies of the corresponding (Moore?) complex for $F$ is the direct limit of those f …

Let $X$ be a smooth projective variety (over an algebraically closed field; it could be the field of complex numbers); $Z$ is its hyperplane section. When there exists an etale $U/X$ such that: $Z$ …

If A is an elliptic curve then G (in your notation) is finite. Yet it seems that for a square of an elliptic curve you get something infinite and very far from being algebraic. If $A=B\times B$, $B$ i …

For a locally closed subscheme $Z\subset X$ (I am interested in the case when $X$ is a variety) one can consider its henselization in $X$ i.e. the 'smallest' pro-etale morphism $U\to X$ such that $Z$ …

It seems that for flag manifolds everything is very easy.:) For other varieties much less is known. For example, recently there was an attempt to construct a counterexample to the Hodge conjecture in …

There is another description for tori. The category of tori over a field F is equivalent to the category of finite-dimensional $G_F$-lattices. Now, there is an operation of induction for group represe …

Assume that a finite group $G$ acts on a quasi-projective variety $Q$ (say, over complex numbers) that possesses a Zariski cover by $\le n$ affine varieties. My question is: does the quotient $Q/G$ ad …

If an equidimensional variety $V$ of dimension $m$ is locally a set-theoretic complete intersection (i.e., it can be covered by open subvarieties of certain intersections of $N-n$ hypersurfaces in $P^ …

Let $M$ be a $R$-linear Chow motif over a field $k$ that is perfect but not necessarily algebraically closed. Can one prove that $M$ is not a direct summand of itself (that is, $M\not\cong M\bigoplus …

Yes, it is.:) Gysin triangles (along with orientable cohomology theories) were studied in detail in several papers of Deglise. For example, have a look at section 4 of http://perso.ens-lyon.fr/frederi …

Well, everything follows from the fact that the total direct image $Rf_*\mathbb{Q}$ splits as the direct sum of its (shifted, co)homology sheaves (so, it is "formal"). Now, this statement can be prove …

For R being a commutative regular excellent Noetherian ring of finite Krull dimension which conditions on $f\in R$ can ensure that the ring $R/(f)$ is regular (so, I want a sufficient condition)? I do …

If you want a tensor product satisfying the isomorphism described, you can just define it as the inductive limit of all finite tensor products. For example, if you tensor $k[x_i]$ like this you really …

You mey be interested in the paper: "Bertini Theorems over Finite Fields"(2002) Bjorn Poonen.

There is a well-known Quillen's localization sequence for (algebraic) K-theory: $\dots\to K_p^Y(X)\to K_p(X)\to K_p(X-Y)\to \dots$, where $Y\to X$ is a closed embedding of schemes. Now suppose that $ …