Search Results

Let $f: X \to Y$ be a morphism between two irreducible schemes and $\mathcal{F}$ sheaf on the small étale site $Y_{ét}$. My question is more or less "dual" to this one: Question: Under which "reasonab …

I have question about a statement found in Etale Cohomology and the Weil Conjecture by Freitag, Kiehl at the end of page 15. It starts with the Remark 1.18 : Let $A$ be a strictly Henselian ring (i.e. …

I have question about a statement from Etale Cohomology and the Weil Conjecture by Freitag, Kiehl at the top of page 16. It seemingly uses the same notations as introduced at the bottom of page 15 and …

Assume $X=\operatorname{Spec}(A)$ is connected and normal (especially integral), and let $g:\eta \hookrightarrow X$ be the inclusion of the generic point of $X$. In Milne's LEC script on Etale Cohomol …

Let $X=\operatorname{Spec}(A)$ be an affine Dedekind domain with field of fractions $K$. Let $\widetilde{A}$ be the integral closure of $A$ in separable closure $ K^{\text{sep}}$. A closed point $x$ o …

I have a question about the verification of remark 1.2 in James Milne's book Étale Cohomology stated on page 156: Assume $X$ be a normal & connected scheme with generic point $g: \eta \to X$. Then the …

Let $f: X \to Y$ be a morphism of schemes and $\mathcal{F}$ sheaf of sets/Abelian groups on the small étale site $Y_{ét}$. Assume we manage somehow to show thatat every geometric point $\overline{y} \ …

I have a question about an argument used in Freitag's and Kiehl's Etale Cohomology and the Weil Conjecture in the proof of: 4.4 Lemma. (p 41) Every sheaf $F$ representable by an étale scheme $U \to X$ …

I have a couple of questions about following proof by Peter Scholze on splitting of the ses (...does it have a name?...) $$0\to I\to\mathrm{Gal}_K\to\mathrm{Gal}_k\to 0$$ for $K$ henselian valuation f …

Let $f:X \to Y$ a surjective smooth proper map between Noetherian schemes and $F$ a locally constant sheaf on small etale site of $X$. Question: Refering to Donu Arapura's answer here, how to see that …

The usual way to define the Henselization $A^h$ of a local ring $(A, \mathfrak{m})$ is by taking the direct limit $\varinjlim (B, \mathfrak q)$ over all étale neighborhoods of $A$ (i.e. pairs $(B,\mat …

Let $X,Y$ be varieties (separated of finite type schemes) over base field $k$, $\mathcal{F}$ be constructible sheaf on $Y_{\mathrm{et}}$ and assume that we have a finite morphism $f: X \to Y$, which g …

Following proof from Milne's Étale Cohomology (page 94) contains an equality I not understand. Setting: assume $X$ is a variety (=absolutely reduced, irreducible scheme of finite type over base field …

I'm studying the book Etale cohomology and the Weil conjecture by Freitag, Kiehl and I have some questions on the subchapter introducing the machinery associating to an étale presheaf a sheaf (that is …

Let $X/k$ be a geometrically connected $k$-variety (=separated of finite type, esp quasi-compact; the base field $k$ assumed to be separable, so $\overline{k}=k^{\text{sep}}$), $\overline{X} := X \oti …