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Let $X$ be a smooth projective connected curve of genus $gge 2$ defined over an algebraically closed field $k$ of characteristic $p>0$. Let $G$ be a finite group, $P$ a Sylow $p$-subgroup of $G$ and $N_G(P)$ its normalizer in $G$. We show that if there exists an etale Galois cover $Yto X$ with group $N_G(P)$, then $G$ is the Galois group wan etale Galois cover $mathcal{Y}tomathcal{X}$, where the genus of $mathcal{X}$ depends on the order of $G$, the number of Sylow $p$-subgroups of $G$ and $g$. Suppose that $G$ is an extension of a group $H$ of order prime to $p$ by a $p$-group $P$ and $X$ is defined over a finite field $mathbb{F}_q$ large enough to contain the $|H|$-th roots of unity. We show that integral idempotent relations in the group ring $mathbb{C}[H]$ imply similar relations among the corresponding generalized Hasse-Witt invariants.
In this article, we show that in each of four standard families of hyperelliptic curves, there is a density-$1$ subset of members with the property that their Jacobians have adelic Galois representation with image as large as possible. This result co
Explicit descriptions of local integral Galois module generators in certain extensions of $p$-adic fields due to Pickett have recently been used to make progress with open questions on integral Galois module structure in wildly ramified extensions of
Let $Pi$ be the fundamental group of a smooth variety X over $F_p$. Given a non-Archimedean place $lambda$ of the field of algebraic numbers which is prime to p, consider the $lambda$-adic pro-semisimple completion of $Pi$ as an object of the groupoi
Let $X$ be an algebraic surface of degree $5$, which is considered as a branch cover of $mathbb{CP}^2$ with respect to a generic projection. The surface has a natural Galois cover with Galois group $S_5$. In this paper, we deal with the fundamental g
We associate to every algebraic number field a hyperbolic surface lamination and an external fundamental group: the latter a generalization of the fundamental germ that necessarily contains external (not first order definable) elements. The external