Ordinary p -adic étale cohomology groups attached to towers of elliptic modular curves. II

Ohta, Masami

doi:10.1007/s002080000119

Cited by 50 publications

(90 citation statements)

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“…Our description is heavily influenced by the approaches of Wiles (1988) and Ohta (2000). Our description is heavily influenced by the approaches of Wiles (1988) and Ohta (2000).…”

Section: Refining the Methods Of Ribet And Mazur-wiles: The Mapmentioning

confidence: 99%

“…As we shall explain in a more canonical fashion in 2.7.6, there is an isomorphism T quo Š S of h-modules given by Ohta's -adic Eichler-Shimura isomorphism (Ohta 1995(Ohta , 2000. Moreover, Ohta showed that T sub Š h via a -duality with T quo .…”

Section: 46mentioning

confidence: 98%

“…To see this, one uses an h-module splitting of the local exact sequence for T Â (see Ohta 2000) and the method of Kurihara (1993) and Harder and Pink (1992). T quo;Eis of the canonical map of 2.4.4 is an isomorphism, or equivalently, that T sub;Eis !…”

Section: 55mentioning

confidence: 99%

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Iwasawa Theory 2012

Bouganis¹,

Venjakob²

2014

Contributions in Mathematical and Computational Sciences

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“…Our description is heavily influenced by the approaches of Wiles (1988) and Ohta (2000). Our description is heavily influenced by the approaches of Wiles (1988) and Ohta (2000).…”

Section: Refining the Methods Of Ribet And Mazur-wiles: The Mapmentioning

confidence: 99%

Section: 46mentioning

confidence: 98%

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Iwasawa Theory 2012

Bouganis¹,

Venjakob²

2014

Contributions in Mathematical and Computational Sciences

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“…SinceH ord 1 is isomorphic by Hida theory to the group of Γ-coinvariants of˜ (see [Oh2,Theorem 1.4.3]), we may apply Nakayama's lemma.…”

Section: Homology Of Modular Curvesmentioning

confidence: 99%

Modular symbols and the integrality of zeta elements

2016

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We consider modifications of Manin symbols in first homology groups of modular curves with p -coefficients for an odd prime p . We show that these symbols generate homology in primitive eigenspaces for the action of diamond operators, with a certain condition on the eigenspace that can be removed on Eisenstein parts. We apply this to prove the integrality of maps taking compatible systems of Manin symbols to compatible systems of zeta elements. In the work of the first two authors on an Iwasawa-theoretic conjecture of the third author, these maps are constructed with certain bounded denominators. As a consequence, their main result on the conjecture was proven after inverting p , and the results of this paper allow one to remove this condition.

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“…With these terminologies, the following theorem follows from [O2],(5.3.18) and (5.3.20): Theorem (3.4.12). Assume that e H(N ; r) M is a Gorenstein ring.…”

Section: Companion Forms and The Structure Of P-adic Hecke Algebras 27mentioning

confidence: 99%

Companion forms and the structure ofp-adic Hecke algebras

Ohta¹

2005

Journal für die reine und angewandte Mathematik (Crelles Journa

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Abstract. We study the structure of the Eiesenstein component of Hida's ordinary p-adic Hecke algebra attached to modular forms, in connection with the companion forms in the space of modular forms (mod p). We show that such an algebra is a Gorenstein ring if certain space of modular forms (mod p) having companions is one-dimensional; and also give a numerical criterion for this one-dimensionality. This in part overlaps with a work of Skinner and Wiles; but our method, based on a work of Ulmer, is totally different. We then consider consequences of the above mentioned Gorenstein property. We especially discuss the connection with the Iwasawa theory.

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Ordinary p -adic étale cohomology groups attached to towers of elliptic modular curves. II

Cited by 50 publications

References 1 publication

Iwasawa Theory 2012

Iwasawa Theory 2012

Modular symbols and the integrality of zeta elements

Companion forms and the structure ofp-adic Hecke algebras

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