Root numbers, Selmer groups, and non-commutative Iwasawa theory
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Publication:3558492
DOI10.1090/S1056-3911-09-00504-9zbMath1213.11135OpenAlexW1963555961MaRDI QIDQ3558492
Takako Fukaya, R. Sujatha, Kazuya Kato, John H. Coates
Publication date: 5 May 2010
Published in: Journal of Algebraic Geometry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s1056-3911-09-00504-9
Elliptic curves over global fields (11G05) Abelian varieties of dimension (> 1) (11G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23)
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Cites Work
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- Regulator constants and the parity conjecture
- Growth of Selmer rank in nonabelian extensions of number fields
- On the Birch-Swinnerton-Dyer quotients modulo squares
- General Selmer groups and critical values of Hecke \(L\)-functions
- Links between cyclotomic and \(\text{GL}_2\) Iwasawa theory
- Completely faithful Selmer groups over Kummer extensions
- \(p\)-divisible groups, finite groups and filtered modules
- On the Euler-Poincaré characteristics of finite dimensional \(p\)-adic Galois representations.
- Finite \(\Lambda\)-submodules of Selmer groups of Abelian varieties over cyclotomic \(\mathbb Z_p\)-extensions.
- Kummer theory for abelian varieties over local fields
- Generalizing the Birch-Stephens theorem. I: Modular curves
- The \(\text{GL}_2\) main conjecture for elliptic curves without complex multiplication
- Parity of ranks for elliptic curves with a cyclic isogeny
- Finding large Selmer rank via an arithmetic theory of local constants
- Sur la dimension cohomologique des groupes profinis
- The parity of the rank of the Mordell-Weil group
- Galois properties of points of finite order of elliptic curves
- The Grothendieck ring of a finite group
- On the parity of ranks of Selmer groups II
- Iwasawa Theory, projective modules, and modular representations
- Computations in non-commutative Iwasawa theory
- A generalisation of the Cassel-Tate pairing.
- Scarcity and abundance of trivial zeros in division towers
- Root numbers of non-abelian twists of elliptic curves
- Galois cohomology of elliptic curves
- Euler characteristics and elliptic curves. II.