On a Conjecture of Tate for Elliptic Surfaces Over Finite Fields

DOI10.1112/plms/s3-69.3.489zbMath0842.14011OpenAlexW2029070921WikidataQ29301312 ScholiaQ29301312MaRDI QIDQ4314441

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Publication date: 14 December 1994

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/plms/s3-69.3.489

zbMATH Keywords

finite fieldDrinfeld modular curvesTate-Shafarevich groupelliptic surfacesEuler systemsBirch and Swinnerton-Dyer conjectureNéron modelselliptic curve over a function fieldDrinfeld-Heegner point

Mathematics Subject Classification ID

Rational points (14G05) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Elliptic surfaces, elliptic or Calabi-Yau fibrations (14J27) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (3)

Birch’s lemma over global function fields ⋮ Higher Heegner points on elliptic curves over function fields. ⋮ On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields

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