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Let $p\ne\ell$ be two prime numbers, and let $K_{\ell}$ be the maximal extension of $\mathbb Q$ ramified only at $\ell$ and $\infty$ (i.e. it is the fixed subfield of $\overline{\mathbb Q}$ by all the …

Let $$ 1\to K\to G\to H\to 1 $$ be an extension of groups. When $K$ is commutative, $H$ acts on $K$ by conjugation; and given groups $K$ and $H,$ with $K$ commutative and $H$ acting on $K,$ such ext …

For adelic points of X (or G), one can first topologize X(Q_p) so that it becomes a p-adic analytic variety, and for almost all p one can define an open subset X(Z_p). Then take X(A) to be the restric …

I think one reason that makes 2 special is that, for the only archimedean place of the rationals, namely the real numbers, it has absolute Galois group of order 2.

Let $z$ be a complex variable and $f(z)$ be a formal power series with rational coefficients (an element in $\mathbb Q[[z]]$), with a finite radius of convergence, and assume $f(z)$ has a meromorphic …

Does anyone know if there's any reference on the $\ell$-adic cohomology of some simple moduli spaces/Shimura varieties, like Siegel moduli varieties $A_{g,N}$ of genus $g$ and level $N,$ for small $g$ …