Anticyclotomic main conjectures for CM modular forms

DOI10.1515/CRELLE.2007.034zbMath1138.11047WikidataQ123011571 ScholiaQ123011571MaRDI QIDQ5421659

Trevor Arnold

Publication date: 24 October 2007

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

zbMATH Keywords

Galois cohomologySelmer groupsEuler system\(p\)-adic \(L\)-functionsIwasawa modulesheight pairing

Mathematics Subject Classification ID

(L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23)

Related Items (10)

The Iwasawa main conjectures for \(\operatorname{GL}_2\) and derivatives of \(p\)-adic \(L\)-functions ⋮ The Birch and Swinnerton-Dyer Conjecture: A brief survey ⋮ Anticyclotomic Iwasawa theory of CM elliptic curves ⋮ Complex multiplication and parity in Iwasawa theory ⋮ Anticyclotomic \(p\)-ordinary Iwasawa theory of elliptic modular forms ⋮ Denominators of Eisenstein cohomology classes for \(\text{GL}_2\) over imaginary quadratic fields ⋮ \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin ⋮ Rubin's conjecture on local units in the anticyclotomic tower at inert primes ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves ⋮ On the anticyclotomic Iwasawa theory of CM forms at supersingular primes

Cites Work

• On the critical values of Hecke \(L\)-functions for imaginary quadratic fields
• On the anticyclotomic main conjecture
• Iwasawa theory and \(p\)-adic heights

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