Anticyclotomic main conjectures

zbMath1200.11082MaRDI QIDQ2369734

Haruzo Hida

Publication date: 20 June 2007

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

Full work available at URL: https://eudml.org/doc/45101

zbMATH Keywords

Eisenstein seriesIwasawa theoryCM abelian varietyMain conjectureCM fieldanticyclotomicBasis problemShimura series

Mathematics Subject Classification ID

Theta series; Weil representation; theta correspondences (11F27) Congruences for modular and (p)-adic modular forms (11F33) Complex multiplication and moduli of abelian varieties (11G15) Fourier coefficients of automorphic forms (11F30) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18) Zeta functions and (L)-functions of number fields (11R42) Iwasawa theory (11R23) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41) Hecke-Petersson operators, differential operators (several variables) (11F60) Galois cohomology (11R34)

Related Items (9)

Coleman-adapted Rubin–Stark Kolyvagin systems and supersingular Iwasawa theory of CM abelian varieties ⋮ Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields ⋮ Image of \(\varLambda \)-adic Galois representations modulo \(p\) ⋮ Growth of Hecke Fields Along a p-Adic Analytic Family of Modular Forms ⋮ Central critical values of modular Hecke \(L\)-functions ⋮ Constancy of adjoint \(\mathcal L\)-invariant ⋮ The Iwasawa \(\mu \)-invariant of \(p\)-adic Hecke \(L\)-functions ⋮ Transcendence of Hecke operators in the big Hecke algebra ⋮ The universal \(p\)-adic Gross-Zagier formula

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