The Eisenstein quotient of the Jacobian variety of a Drin'feld modular curve.

DOI10.2977/prims/1195164439zbMath1045.11510OpenAlexW2071913213MaRDI QIDQ1897732

Akio Tamagawa

Publication date: 22 October 1995

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195164439

Mathematics Subject Classification ID

(L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Drinfel'd modules; higher-dimensional motives, etc. (11G09) Arithmetic ground fields for abelian varieties (14K15)

Related Items (9)

An explicit basis of modular symbols on function fields ⋮ \(\mathcal D\)-elliptic sheaves and odd Jacobians ⋮ On the Eisenstein ideal over function fields ⋮ ON THE EISENSTEIN IDEAL OF DRINFELD MODULAR CURVES ⋮ On the torsion of Drinfeld modules of rank two ⋮ On component groups of Jacobians of Drinfeld modular curves. ⋮ A finiteness conjecture on abelian varieties with constrained prime power torsion ⋮ Pesenti-Szpiro inequality for optimal elliptic curves ⋮ On the degree of modular parametrizations over function fields.

Cites Work

• Structure theorems for group-varieties
• Two-dimensional \(\ell\)-adic representations of the Galois group of a global field of characteristic \(p\) and automorphic forms on \(\mathrm{GL}(2)\)
• Modular symbols for \(F_ q(T)\)
• Endomorphisms of semi-stable Abelian varieties over number fields
• Zur Vermutung von Birch und Swinnerton-Dyer über globalen Funktionenkoerpern
• Good reduction of abelian varieties
• Algebraic number fields and symplectic discontinuous groups
• Dirichlet series and automorphic forms
• Automorphic forms on GL (2)
• On some results of Atkin and Lehner
• Les Constantes des Equations Fonctionnelles des Fonctions L
• Some Basic Theorems on Algebraic Groups
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