Iwasawa-theory of abelian varieties at primes of non-ordinary reduction

DOI10.1007/BF02570472zbMath0847.14026MaRDI QIDQ1895741

Heiko Knospe

Publication date: 29 August 1995

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156085

zbMATH Keywords

Birch and Swinnerton-Dyer conjectures\(p\)-adic \(L\)-function of an abelian variety

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Varieties over finite and local fields (11G25) Zeta functions and (L)-functions (11S40) Algebraic theory of abelian varieties (14K05)

Related Items (6)

Anticyclotomic Iwasawa theory of abelian varieties of \(\mathrm{GL}_2\)-type at non-ordinary primes ⋮ Bounds on the Tamagawa numbers of a crystalline representation over towers of cyclotomic extensions ⋮ A generalization of the theory of Coleman power series ⋮ Ranks of rational points of the Jacobian varieties of hyperelliptic curves ⋮ On the vanishing of Selmer groups for elliptic curves over ring class fields ⋮ The p-Adic Height Pairing on Abelian Varieties at Non-ordinary Primes

Cites Work

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• Théorie d'Iwasawa p-adique locale et globale. (Local and global p-adic Iwasawa theory)
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• \(p\)-adic height pairings. II
• Arithmetic of formal groups and applications. I: Universal norm subgroups
• \(p\)-adic \(L\)-functions of an elliptic curve and rational points
• Iwasawa theory of \(p\)-adic representations over a local field
• Iwasawa L-functions of varieties over algebraic number fields. A first approach
• Rational points of Abelian varieties with values in towers of number fields
• Lectures on \(p\)-divisible groups
• CYCLOTOMIC FIELDS AND MODULAR CURVES

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