Main conjectures for higher rank nearly ordinary families -- I

Büyükboduk, Kâzım; Ochiai, Tadashi

doi:10.48550/arxiv.1708.04494

Cited by 2 publications

(2 citation statements)

References 27 publications

(33 reference statements)

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“…The next immediate goal is to prove a version of the Iwasawa main conjecture for our GU(2, 1)-representation V . We do so by using results from [BO17], which generalise the standard Euler system machinery from [MR04, §5] to work over any base number field K and to allow more general Panchishkin local conditions. In order to apply these results, we need to place some conditions on V in addition to ordinarity at all primes above p.…”

Section: Bounding Selmer Groupsmentioning

confidence: 99%

Euler Systems and Selmer Bounds for GU(2,1)

Manji¹

2022

Preprint

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We investigate properties of the Euler system associated to certain automorphic representations of the unitary similitude group GU(2,1) with respect to an imaginary quadratic field E, constructed by Loeffler-Skinner-Zerbes. By adapting Mazur and Rubin's Euler system machinery we prove one divisibility of the "rank 1" Iwasawa main conjecture under some mild hypotheses. When p is split in E we also prove a "rank 0" statement of the main conjecture, bounding a particular Selmer group in terms of a p-adic distribution conjecturally interpolating complex L-values. We then prove descended versions of these results, at integral level, where we bound certain Bloch-Kato Selmer groups. We will also discuss the case where p is inert, which is a work in progress.

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Section: Bounding Selmer Groupsmentioning

confidence: 99%

Euler Systems and Selmer Bounds for GU(2,1)

Manji¹

2022

Preprint

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“…Remark 1.1. Buyukboduk and Ochiai [5], employing the Euler system of Beilinson-Flach elements constructed by Kings-Loeffler-Zerbes [25], have proved that, under certain technical hypotheses, the inequality ≤ in (IMC) holds for the Galois representation ρ 4 4 4,3 .…”

Section: MCmentioning

confidence: 99%

Codimension two cycles in Iwasawa theory and tensor product of Hida families

Lei

Palvannan

2019

Preprint

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The purpose of this paper is to build on results in higher codimension Iwasawa theory. The setting of our results involves Galois representations arising as cyclotomic twist deformations associated to (i) the tensor product of two cuspidal Hida families F and G, and (ii) the tensor product of three cuspidal Hida families F , G and H. On the analytic side, we consider (i) a pair of 3-variable Rankin-Selberg p-adic L-functions constructed by Hida and (ii) a balanced 4-variable p-adic L-function (whose construction is forthcoming in a work of Hsieh and Yamana) and an unbalanced 4-variable p-adic L-function (whose existence is currently conjectural). In each of these setups, when the two p-adic L-functions generate a height two ideal in the corresponding deformation ring, we use codimension two cycles of that ring to relate them to a pair of pseudo-null modules. 4 Description of Z(Q, D d d d,n ) and Z(Q, D ⋆ d d d,n

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Main conjectures for higher rank nearly ordinary families -- I

Cited by 2 publications

References 27 publications

Euler Systems and Selmer Bounds for GU(2,1)

Euler Systems and Selmer Bounds for GU(2,1)

Codimension two cycles in Iwasawa theory and tensor product of Hida families

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