\(p\)-descent in characteristic \(p\)

DOI10.1215/S0012-7094-91-06210-1zbMath0742.14028OpenAlexW1511302673MaRDI QIDQ1814238

Douglas L. Ulmer

Publication date: 25 June 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-91-06210-1

zbMATH Keywords

rational pointsconjecture of Birch and Swinnerton-DyerSelmer groupIgusa curvesMordell-Weil theorem\(L\)- function\(p\)-descent

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Rational points (14G05) Arithmetic ground fields for curves (14H25) Elliptic curves (14H52) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10)

Related Items (10)

On the Fourier coefficients of modular forms. II ⋮ Exact holomorphic differentials on a quotient of the Ree curve ⋮ Local-global principles for Weil–Châtelet divisibility in positive characteristic ⋮ Curves and Jacobians over Function Fields ⋮ Parity conjectures for elliptic curves over global fields of positive characteristic ⋮ Superspecial rank of supersingular abelian varieties and Jacobians ⋮ On \(BT_1\) group schemes and Fermat curves ⋮ CONTROL THEOREMS FOR ELLIPTIC CURVES OVER FUNCTION FIELDS ⋮ On the Brauer-Siegel ratio for abelian varieties over function fields ⋮ Computation of Mordell–Weil bases for ordinary elliptic curves in characteristic two

Cites Work

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• On universal elliptic curves over Igusa curves
• Congruences entre séries d'Eisenstein, dans le cas supersingulier
• A tameness criterion for Galois representations associated to modular forms (mod \(p\))
• A Study of the Local Components of the Hecke Algebra mod l
• L-Functions of Universal Elliptic Curves Over Igusa Curves
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• Two-Descent for Elliptic Curves in Characteristic Two
• The first de Rham cohomology group and Dieudonné modules
• Group schemes of prime order

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