Results 41 to 50 of about 775 (194)

On the section conjecture over fields of finite type

Mathematische Nachrichten, Volume 298, Issue 11, Page 3476-3493, November 2025.
Abstract Assume that the section conjecture holds over number fields. We prove then that it holds for a broad class of curves defined over finitely generated extensions of Q$\mathbb {Q}$. This class contains every projective, hyperelliptic curve, every hyperbolic, affine curve of genus ≤2$\le 2$, and a basis of open subsets of any curve.
Giulio Bresciani
wiley   +1 more source

Normal covering numbers for Sn$S_n$ and An$A_n$ and additive combinatorics

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3307-3325, November 2025.
Abstract The normal covering number γ(G)$\gamma (G)$ of a noncyclic group G$G$ is the minimum number of proper subgroups whose conjugates cover the group. We give various estimates for γ(Sn)$\gamma (S_n)$ and γ(An)$\gamma (A_n)$ depending on the arithmetic structure of n$n$. In particular we determine the limsups over γ(Sn)/n$\gamma (S_n) / n$ and γ(An)
Sean Eberhard, Connor Mellon
wiley   +1 more source

Galois Module Structure and Elliptic Functions

Journal of Number Theory, 1995
The subject of this paper is the problem of determining the Galois module structure of rings of integers \({\mathcal O}_L\) of abelian extensions \(L\) of a number field \(K\). By a classical result of Leopoldt \({\mathcal O}_L\) is free as a module over the associated order.
openaire   +3 more sources

Arithmetic sparsity in mixed Hodge settings

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3511-3521, November 2025.
Abstract Let X$X$ be a smooth irreducible quasi‐projective algebraic variety over a number field K$K$. Suppose X$X$ is equipped with a p$p$‐adic étale local system compatible with an admissible graded‐polarized variation of mixed Hodge structures on the complex analytification of XC$X_{\operatorname{\mathbb {C}}}$.
Kenneth Chung Tak Chiu
wiley   +1 more source

The geometry and arithmetic of bielliptic Picard curves

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
wiley   +1 more source

Integral Galois module structure for elementary abelian extensions with a Galois scaffold [PDF]

Proceedings of the American Mathematical Society, 2014
This paper justifies an assertion in (Elder, Proc AMS 137 (2009), no 4, 1193--1203) that Galois scaffolds make the questions of Galois module structure tractable. Let $k$ be a perfect field of characteristic $p$ and let $K=k((T))$. For the class of characteristic $p$ elementary abelian $p$-extensions $L/K$ with Galois scaffolds described in mentioned ...
Byott, Nigel P., Elder, G. Griffith
openaire   +3 more sources

A note on local formulae for the parity of Selmer ranks

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3112-3132, October 2025.
Abstract In this note, we provide evidence for a certain ‘twisted’ version of the parity conjecture for Jacobians, introduced in prior work of Dokchitser, Green, Konstantinou and the author. To do this, we use arithmetic duality theorems for abelian varieties to study the determinant of certain endomorphisms acting on p∞$p^\infty$‐Selmer groups.
Adam Morgan
wiley   +1 more source

Lubin-Tate moduli space of semisimple mod p Galois representations for GL_2 and Hecke modules [PDF]

, 2023
Cédric Pépin, Tobias Schmidt
openalex   +1 more source

GALOIS GROUPS OF MODULES AND INVERSE POLYNOMIAL MODULES [PDF]

Bulletin of the Korean Mathematical Society, 2007
Given an injective envelope E of a left R-module M, there is an associative Galois group Gal. Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope of an inverse polynomial module as a left R[x]-module and we can define an associative Galois group Gal.
Sang-Won Park, Jin-Sun Jeong
openaire   +1 more source

Motivic p$p$‐adic tame cohomology

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3194-3210, October 2025.
Abstract We construct a comparison functor between (A1$\mathbf {A}^1$‐local) tame motives and (□¯${\overline{\square }}$‐local) log‐étale motives over a field k$k$ of positive characteristic. This generalizes Binda–Park–Østvær's comparison for the Nisnevich topology.
Alberto Merici
wiley   +1 more source