Selmer groups for elliptic curves in -extensions of function fields of characteristic

A Bandini, I Longhi - Annales de l'institut Fourier, 2009 - numdam.org
Let F be a function field of characteristic p> 0, F/F a Zd l-extension (for some prime l= p) and
E/F a non-isotrivial elliptic curve. We study the behaviour of the r-parts of the Selmer groups …

[PDF][PDF] Contributions à l'étude des formes modulaires sur les corps de fonctions

C Armana - 2024 - hal.science
L'arithmétique des corps de fonctions est apparue au XIXe siècle en parallèle de la théorie
des nombres dite classique. Sa naissance et son développement se fondent sur de …

FUNCTIONAL EQUATION OF CHARACTERISTIC ELEMENTS OF ABELIAN VARIETIES OVER FUNCTION FIELDS (ℓ≠ p)

A Pal - International Journal of Number Theory, 2014 - World Scientific
In this paper we apply methods from the number field case of Perrin-Riou [20] and Zábrádi
[32] in the function field setup. In ℤℓ-and GL2-cases (ℓ≠ p), we prove algebraic functional …

Aspects of Iwasawa theory over function fields

A Bandini, F Bars, I Longhi - arXiv preprint arXiv:1005.2289, 2010 - arxiv.org
We consider $\mathbb {Z} _p^{\mathbb {N}} $-extensions $\mathcal {F} $ of a global function
field $ F $ and study various aspects of Iwasawa theory with emphasis on the two main …

The Rigid Analytical Regulator and K2 of Drinfeld Modular Curves

A Pál - Publications of the Research Institute for Mathematical …, 2010 - ems.press
We evaluate a rigid analytical analogue of the Beilinson–Bloch–Deligne regulator on certain
explicit elements in the _K_2 of Drinfeld modular curves, constructed from analogues of …

Une base explicite de symboles modulaires sur les corps de fonctions

C Armana - Journal für die reine und angewandte Mathematik …, 2016 - degruyter.com
Les symboles modulaires pour le sous-groupe Γ 0⁢(𝔫) de GL 2⁢(𝔽 q⁢[T]), définis par
Teitelbaum, possèdent une présentation par un nombre fini de générateurs et relations …

An efficient algorithm to compute an elliptic curve from a corresponding function field automorphic form

Y Bermudez Tobon - 2015 - archiv.ub.uni-heidelberg.de
Elliptic modular forms of weight 2 and elliptic modular curves are strongly related. In the rank-
2 Drinfeld module situation, we have still modular curves that can be described analytically …

Sur les symboles modulaires de Manin–Teitelbaum pour Fq (T)

C Armana - Comptes Rendus Mathematique, 2009 - Elsevier
The group of modular symbols for Fq (T), as defined by Teitelbaum, has a presentation given
by generators, called Manin–Teitelbaum symbols, and relations. We give a formula for the …