Results 71 to 80 of about 5,346 (174)

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

On fixed‐point‐free involutions in actions of finite exceptional groups of Lie type

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract Let G$G$ be a nontrivial transitive permutation group on a finite set Ω$\Omega$. By a classical theorem of Jordan, G$G$ contains a derangement, which is an element with no fixed points on Ω$\Omega$. Given a prime divisor r$r$ of |Ω|$|\Omega |$, we say that G$G$ is r$r$‐elusive if it does not contain a derangement of order r$r$. In a paper from
Timothy C. Burness, Mikko Korhonen
wiley   +1 more source

Supersingular K3 Surfaces are Unirational

, 2014
We show that supersingular K3 surfaces in characteristic $p\geq5$ are related by purely inseparable isogenies. This implies that they are unirational, which proves conjectures of Artin, Rudakov, Shafarevich, and Shioda.
Liedtke, Christian
core   +1 more source

Cyclic cubic points on higher genus curves

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract The distribution of degree d$d$ points on curves is well understood, especially for low degrees. We refine this study to include information on the Galois group in the simplest interesting case: d=3$d = 3$. For curves of genus at least 5, we show cubic points with Galois group C3$C_3$ arise from well‐structured morphisms, along with providing ...
James Rawson
wiley   +1 more source

Pure Anderson Motives and Abelian \tau-Sheaves

, 2010
Pure t-motives were introduced by G. Anderson as higher dimensional generalizations of Drinfeld modules, and as the appropriate analogs of abelian varieties in the arithmetic of function fields.
G. Anderson, G. Anderson, J. Tate, M. Papanikolas, Matthias Bornhofen, R. Pink, Urs Hartl, V.G. Drinfeld, V.G. Drinfeld, V.G. Drinfeld, W.C. Waterhouse, Y. Taguchi, Y. Taguchi   +12 more
core   +1 more source

Parity of ranks of Jacobians of curves

Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.
Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser, Holly Green, Alexandros Konstantinou, Adam Morgan   +3 more
wiley   +1 more source

Mazur's isogeny theorem

, 2022
Mazur's isogeny theorem states that if $p$ is a prime for which there exists an elliptic curve $E / \mathbb{Q}$ that admits a rational isogeny of degree $p$, then $p \in \{2,3,5,7,11,13,17,19,37,43,67,163 \}$. This result is one of the cornerstones of the theory of elliptic curves and plays a crucial role in the proof of Fermat's Last Theorem.
openaire   +2 more sources

Multiplicative isogeny estimates [PDF]

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1998
AbstractThe theory of isogeny estimates for Abelian varieties provides ‘additive bounds’ of the form ‘d is at most B’ for the degrees d of certain isogenies. We investigate whether these can be improved to ‘multiplicative bounds’ of the form ‘d divides B’.
openaire   +3 more sources

Spectra of subrings of cohomology generated by characteristic classes for fusion systems

Bulletin of the London Mathematical Society, Volume 57, Issue 7, Page 1990-2005, July 2025.
Abstract If F$\mathcal {F}$ is a saturated fusion system on a finite p$p$‐group S$S$, we define the Chern subring Ch(F)${\operatorname{Ch}}(\mathcal {F})$ of F$\mathcal {F}$ to be the subring of H∗(S;Fp)$H^*(S;{\mathbb {F}}_p)$ generated by Chern classes of F$\mathcal {F}$‐stable representations of S$S$. We show that Ch(F)${\operatorname{Ch}}(\mathcal {
Ian J. Leary, Jason Semeraro
wiley   +1 more source

Application of hierarchic authentication to isogenies of elliptic curves for providing safety of data routing in the systems of analysis of digital production traffica

SHS Web of Conferences, 2018
The article discusses the peculiarities of the process of information routing in the course of acquisition and processing big data of digital production, including systems of traffic analysis.
Alexandrova Elena, Poltavtseva Maria, Yarmak Anastasia   +2 more
doaj   +1 more source