Search Results

We can via the bar construction canonically associate to a monoid $A$ the nerve $N(B A)$, a simplicial set with $N(\mathbf{B}A)_k := \times^{k+1} A $ and canonical face maps and degeneracy maps induc …

Let $X$ be an integral locally noetherian smooth scheme over base field $k$. Then for every $x \in X^{(1)}$ point of codimension $1$, the stalk $\mathcal{O}_{X,x}$ is a discrete valuation ring. Choos …

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 …

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 $\mathcal{A}$ be an additive category and $B \to C$ a nonzero map. Are there say "standard" techniques & criteria one should keep in mind when working with additive categories to attack the questi …

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 …

Let $R$ be a commutative ring with one and $S$ commutative faithfully flat $R$-algebra (that is there is a faithfully flat ring map let $\phi: R \to S$). Then the so called Amitsur complex $R \to S^{ …

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 …

That's the second part of my coarse becoming acquainted with Henselizations of fields and local rings. (in this question we focus on local rings as it is more algebro geometric motivated). So let $(R …

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 …

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 …

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 question about techniques used in determining the stratification over which a constructible sheaf falls into even constant pieces demonstrated on this example from Wikipedia. Let $f:X = \text …

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 …

Let $S = \operatorname{Spec} R$ an affine scheme (in our case latter a complete dvr) and $p$ a prime. Then Barsotti-Tate group or $p$-divisible group $G$ of height $h$ over $S$ is an inductive system …