Euler systems, Iwasawa theory, and Selmer groups

DOI10.2996/kmj/1138044090zbMath0993.11033OpenAlexW2067272590MaRDI QIDQ1975395

Kazuya Kato

Publication date: 26 September 2002

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

Full work available at URL: https://doi.org/10.2996/kmj/1138044090

zbMATH Keywords

Galois representationsEuler systemSelmer group\(p\)-adic representationfiniteness theoremsanalogue of Iwasawa main conjecturesecond étale cohomology

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (p)-adic theory, local fields (11F85) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Symbols and arithmetic ((K)-theoretic aspects) (19F15)

Related Items

The Bloch-Kato conjecture on special values of \(L\)-functions. A survey of known results., Bloch-Kato conjecture and Main Conjecture of Iwasawa theory for Dirichlet characters, The Tamagawa number conjecture of adjoint motives of modular forms, Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms, On the \(p\)-adic Birch, Swinnerton-Dyer conjecture for non-semistable reduction, Euler system for Galois deformations., Tamagawa defect of Euler systems, On higher fitting ideals of certain Iwasawa modules associated with Galois representations and Euler systems, Arithmetic of elliptic curves and diophantine equations, Stickelberger elements and Kolyvagin systems, Torsion des courbes elliptiques sur les corps cubiques. (Torsion of elliptic curves over cubic fields), Specialization method in Krull dimension two and Euler system theory over normal deformation rings, \(K\)-theory of curves over number fields

Cites Work

• On certain types of \(p\)-adic representations of the Galois group of a local field; construction of a Barsott-Tate ring.
• Class fields of abelian extensions of \(\mathbb Q\)
• Higher regulators and values of \(L\)-functions
• The ``main conjectures of Iwasawa theory for imaginary quadratic fields
• La conjecture de Weil. I
• \(p\)-adic analytic groups
• FINITENESS OF $ E(\mathbf{Q})$ AND $ \textrm{Ø}(E,\mathbf{Q})$ FOR A SUBCLASS OF WEIL CURVES
• Stark units and Kolyvagin's „Euler Systems“
• Notes on Crystalline Cohomology. (MN-21)
• Notes on étale cohomology of number fields
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