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There are lots of references on global unramified geometric class field theory (following Deligne's $\ell$-adic sheaves approach). There are also some notes talking about how to extend Deligne's ...

Over number fields, we have two natural degeneracy maps $$X_0(N)\leftarrow X_0(pN) \rightarrow X_0(N)$$ between the (compactified) moduli space of elliptic curves with level $pN$ and $N$ respectively (...

Let $F$ be a function field with one variable with total constant field $k$, and let $X$ be the set of all places of $F$. How do I show that the genus of $k(T)$ is $0$ without using Riemann-Roch? Is ...