Root numbers and ranks in positive characteristic

DOI10.1016/j.aim.2005.06.013zbMath1113.11033arXivmath/0408153OpenAlexW1969231434MaRDI QIDQ2577011

Keith Conrad, Brian Conrad, Harald Andrés Helfgott

Publication date: 29 December 2005

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408153

zbMATH Keywords

elliptic curveroot numberfunction fields.

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Global ground fields in algebraic geometry (14G25)

Related Items (16)

Elliptic curves with all cubic twists of the same root number ⋮ Non-isotrivial elliptic surfaces with non-zero average root number ⋮ The inverse Galois problem for orthogonal groups ⋮ ON THE FIBRES OF AN ELLIPTIC SURFACE WHERE THE RANK DOES NOT JUMP ⋮ Root number in Integer parameter families of elliptic curves ⋮ Superficies elípticas y el décimo problema de Hilbert ⋮ Root numbers and parity phenomena ⋮ On the variation of the root number in families of elliptic curves ⋮ Rational equivalences on products of elliptic curves in a family ⋮ Prime specialization in higher genus I ⋮ Computing the average root number of an elliptic surface ⋮ On the density of rational points on rational elliptic surfaces ⋮ Tamagawa numbers of elliptic curves with prescribed torsion subgroup or isogeny ⋮ On elliptic curves with complex multiplication and root numbers ⋮ A GENERALIZATION OF THE CONGRUENT NUMBER PROBLEM ⋮ Galois groups arising from families with big orthogonal monodromy

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