Explicit Selmer groups for cyclic covers of ℙ¹

Michael Stoll; Ronald van Luijk

Displaying similar documents to “Explicit Selmer groups for cyclic covers of ℙ¹”

A characterization of Eisenstein polynomials generating extensions of degree $p^{2}$ and cyclic of degree $p^{3}$ over an unramified $𝔭$ -adic field

Maurizio Monge (2014)

Journal de Théorie des Nombres de Bordeaux

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Let $p \neq 2$ be a prime. We derive a technique based on local class field theory and on the expansions of certain resultants allowing to recover very easily Lbekkouri’s characterization of Eisenstein polynomials generating cyclic wild extensions of degree $p^{2}$ over $ℚ_{p}$ , and extend it to when the base fields $K$ is an unramified extension of $ℚ_{p}$ . When a polynomial satisfies a subset of such conditions the first unsatisfied condition characterizes the Galois group of the normal closure. We...

Noncommutative numerical motives, Tannakian structures, and motivic Galois groups

Matilde Marcolli, Gonçalo Tabuada (2016)

Journal of the European Mathematical Society

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In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum ${(k)}_{F}$ of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum ${(k)}_{F}$ is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined...

A characterization of the linear groups $L_{2} (p)$

Alireza Khalili Asboei, Ali Iranmanesh (2014)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group and $π_{e} (G)$ be the set of element orders of $G$ . Let $k \in π_{e} (G)$ and $m_{k}$ be the number of elements of order $k$ in $G$ . Set $nse (G) : = {m_{k} : k \in π_{e} (G)}$ . In fact $nse (G)$ is the set of sizes of elements with the same order in $G$ . In this paper, by $nse (G)$ and order, we give a new characterization of finite projective special linear groups $L_{2} (p)$ over a field with $p$ elements, where $p$ is prime. We prove the following theorem: If $G$ is a group such that $| G | = | L_{2} (p) |$ and $nse (G)$ consists of $1$ , $p^{2} - 1$ , $p (p + ϵ) / 2$ and some numbers divisible by $2 p$ , where $p$ is a prime...

On quotients of the space of orderings of the field ℚ(x)

Paweł Gładki, Bill Jacob (2016)

Banach Center Publications

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In this paper we present a method of obtaining new examples of spaces of orderings by considering quotient structures of the space of orderings $(X_{ℚ (x)}, G_{ℚ (x)})$ - it is, in general, nontrivial to determine whether, for a subgroup $G ₀ \subset G_{ℚ (x)}$ the derived quotient structure $(X_{ℚ (x)} |_{G ₀}, G ₀)$ is a space of orderings, and we provide some insights into this problem. In particular, we show that if a quotient structure arising from a subgroup of index 2 is a space of orderings, then it necessarily is a profinite one.

Moufang loops of order coprime to three that cyclically extend groups of dihedral type

Aleš Drápal (2016)

Commentationes Mathematicae Universitatis Carolinae

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This paper completely solves the isomorphism problem for Moufang loops $Q = G C$ where $G ⊴ Q$ is a noncommutative group with cyclic subgroup of index two and $| Z (G) | \leq 2$ , $C$ is cyclic, $G \cap C = 1$ , and $Q$ is finite of order coprime to three.

Fields of moduli of three-point $G$ -covers with cyclic $p$ -Sylow, II

Andrew Obus (2013)

Journal de Théorie des Nombres de Bordeaux

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We continue the examination of the stable reduction and fields of moduli of $G$ -Galois covers of the projective line over a complete discrete valuation field of mixed characteristic $(0, p)$ , where $G$ has a $p$ -Sylow subgroup $P$ of order $p^{n}$ . Suppose further that the normalizer of $P$ acts on $P$ via an involution. Under mild assumptions, if $f : Y \to ℙ^{1}$ is a three-point $G$ -Galois cover defined over $\bar{ℚ}$ , then the $n$ th higher ramification groups above $p$ for the upper numbering of the (Galois closure of...

An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors

Amit Hogadi, Supriya Pisolkar (2013)

Acta Arithmetica

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Let L/K be a finite Galois extension of complete discrete valued fields of characteristic p. Assume that the induced residue field extension $k_{L} / k_{K}$ is separable. For an integer n ≥ 0, let $W_{n} (_{L})$ denote the ring of Witt vectors of length n with coefficients in $_{L}$ . We show that the proabelian group ${H^{1} (G, W_{n} (_{L}))}_{n \in ℕ}$ is zero. This is an equicharacteristic analogue of Hesselholt’s conjecture, which was proved before when the discrete valued fields are of mixed characteristic.

Bounded cohomology and isometry groups of hyperbolic spaces

Ursula Hamenstädt (2008)

Journal of the European Mathematical Society

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Let $X$ be an arbitrary hyperbolic geodesic metric space and let $Γ$ be a countable subgroup of the isometry group $Iso (X)$ of $X$ . We show that if $Γ$ is non-elementary and weakly acylindrical (this is a weak properness condition) then the second bounded cohomology groups $H_{b}^{2} (Γ, ℝ)$ , $H_{b}^{2} (Γ, ℓ^{p} (Γ))$ $(1 < p < \infty)$ are infinite dimensional. Our result holds for example for any subgroup of the mapping class group of a non-exceptional surface of finite type not containing a normal subgroup which virtually splits as a direct...

Eigenspaces of the ideal class group

Cornelius Greither, Radan Kučera (2014)

Annales de l’institut Fourier

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The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field $F$ and an odd prime $p$ dividing the degree $[F : ℚ]$ assuming that the $p$ -part of $Gal (F / ℚ)$ group is cyclic.