Local-global aspects of (hyper)elliptic curves over (in)finite fields
Advances in Mathematics of Communications, 2010 We survey the interaction between local and global theory for studying the arithmetic properties of curves, jacobians, and abelian varieties.
openaire +1 more source
Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
, 2019 We analyse the Weak Gravity Conjecture for chiral four-dimensional F-theory compactifications with N=1 supersymmetry. Extending our previous work on nearly tensionless heterotic strings in six dimensions, we show that under certain assumptions a tower of
Lee, Seung-Joo +2 more
core +1 more source
On the modularity of elliptic curves over a composite field of some real quadratic fields
, 2016 Let $K$ be a composite field of some real quadratic fields.
Yoshikawa, Sho
core +1 more source
Some remarks concerning points of finite order on elliptic curves over global fields
Arkiv för Matematik, 1977 Using the reduction theory of Nrron we give necessary conditions for the existence of points of order q on elliptic curves E rational over global fields. An application is the determination of all elliptic cu rves /Q with integer j and torsion points, generalizing Olson [8]. Another application is a theorem about semistable reduction whose consequences
openaire +3 more sources
Can a Drinfeld module be modular?
, 2002 Let $k$ be a global function field with field of constants $\Fr$ and let $\infty$ be a fixed place of $k$. In his habilitation thesis \cite{boc2}, Gebhard B\"ockle attaches abelian Galois representations to characteristic $p$ valued cusp eigenforms and ...
Goss, David
core +3 more sources
Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields
9 pages; Title has changed; We have added referees' comments;
Gajović, Stevan +2 more
openaire +2 more sources
A Hasse principle of the higher chow groups for an elliptic curve over a global function field
We investigate the structure of the higher Chow groups $CH^2(E,1)$ for an elliptic curve $E$ over a global function field $F$. Focusing on the kernel $V(E)$ of the push-forward map $CH^2(E,1)\to F^{\times}$ associated to the structure map $E\to \operatorname{Spec}(F)$, we analyze the torsion part $V(E)$ based on the mod $l$ Galois representations ...
openaire +2 more sources
On the second rational K -group of an elliptic curve over global fields of positive characteristic [PDF]
Proceedings of the London Mathematical Society, 2011 Satoshi Kondo, Seidai Yasuda
openaire +1 more source
Local-global principle for isogenies of elliptic curves over quadratic fields
In this paper, we prove that the local-global principle of 11-isogenies for elliptic curves over quadratic fields does not fail. This gives a positive answer to a conjecture by Banwait and Cremona. The proof is based on the determination of the set of quadratic points on the modular curve XD10(11).
Gajović, S. ; https://orcid.org/0000-0003-3846-5199 +2 more
openaire +1 more source
The 3d Mixed BF Lagrangian 1-Form: A Variational Formulation of Hitchin's Integrable System. [PDF]
Commun Math PhysCaudrelier V +3 more
europepmc +1 more source