All Questions

Let $X$ be a variety over a number field $K$. Then it is known that for any topological covering $X' \to X(\mathbb{C})$, the topological space $X'$ can be given the structure of a $\overline{K}$-...

Which of the following operations on étale sheaves $A$ commute with tensor powers? (eg. for instance $i^*(A^{\otimes n})=(i^*(A))^{\otimes n}$?) $i^*(A)$, $i$ closed immersion. $i_*(A)$ $i^!(A)$ $i_!(...

Here are four possible definitions for an etale, finite, surjective map $X\rightarrow Y$ between integral schemes to be considered Galois: There exists a finite group $G$, and an action $\varphi: G\...

Define an arithmetic scheme $X$ to be a separated, integral scheme, flat and finite type over $\mathbb{Z}$. I am interested in obtaining examples of finite étale covers of arithmetic schemes. I am ...

Let $X$ be a regular noetherian scheme of dimension one. Let $d$ be an integer. Question. Are there only finitely many finite etale morphisms $Y\to X$ of degree $d$? I want to exclude finite etale ...

Let $X$ be a (smooth projective geometrically connected) curve over a number field $K$ of genus $g\geq 2$. Let $d\geq 2$ be an integer. Does there exist a curve $Y$ over $K$ with a finite etale $K$-...