Results 51 to 60 of about 6,385 (201)
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
A Compact and Scalable Hardware/Software Co-design of SIKE
Transactions on Cryptographic Hardware and Embedded Systems, 2020 We present efficient and compact hardware/software co-design implementations of the Supersingular Isogeny Key Encapsulation (SIKE) protocol on field-programmable gate arrays (FPGAs).
Pedro Maat C. Massolino +3 more
doaj +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
CM points on Shimura curves via QM-equivariant isogeny volcanoes [PDF]
, 2022 Frederick Saia
openalex +1 more source
Computing isogenies between abelian varieties [PDF]
Compositio Mathematica, 2012 AbstractWe describe an efficient algorithm for the computation of separable isogenies between abelian varieties represented in the coordinate system given by algebraic theta functions. Let A be an abelian variety of dimension g defined over a field of odd characteristic. Our algorithm comprises two principal steps. First, given a theta null point for A
Lubicz, David, Robert, Damien
openaire +5 more sources
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
Renormalization, Isogenies, and Rational Symmetries of Differential Equations
Advances in Mathematical Physics, 2010 We give an example of infinite-order rational transformation that leaves a linear differential equation covariant. This example can be seen as a nontrivial but still simple illustration of an exact representation of the renormalization group.
A. Bostan +6 more
doaj +1 more source
Computing endomorphism rings of abelian varieties of dimension two [PDF]
, 2012 Generalizing a method of Sutherland and the author for elliptic curves, we design a subexponential algorithm for computing the endomorphism rings of ordinary abelian varieties of dimension two over finite fields.
Bisson, Gaetan
core +5 more sources
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 +3 more
wiley +1 more source