Codimension two cycles in Iwasawa theory and elliptic curves with supersingular reduction

Lei, Antonio; Palvannan, Bharathwaj

doi:10.48550/arxiv.1806.07214

Cited by 3 publications

(17 citation statements)

References 31 publications

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“…See section 4 in [31] for some such examples. Contrast this with earlier results in higher codimension Iwasawa theory [2,28], which were obtained over regular local rings. Without assuming the Iwasawa-Greenberg main conjecture, the following subtle question arises: Question 1.2.…”

Section: Selmer Groups and Principal Divisorscontrasting

confidence: 99%

“…The main impetus behind our results in this paper and prior results in higher codimension Iwasawa theory [2,28], are pseudo-nullity conjectures in Iwasawa theory. These conjectures are briefly recalled in Section 1.3.…”

Section: MCsupporting

confidence: 55%

“…We will explain the notations that we have used and some of the motivation behind the hypotheses that we have imposed after the statement of Theorem 1. This theorem follows from Theorem 4.3 of our earlier work [28]. This is explained in Section 5.…”

Section: Main Results In Higher Codimension Iwasawa Theorymentioning

confidence: 63%

“…). The main result in an earlier work of ours (Theorem 1 in [28]) is motivated by the following pseudo-nullity conjecture, which is a special case of a conjecture due to Coates and Sujatha (Conjecture B in [6]):…”

Section: Pseudo-nullity Conjectures In Iwasawa Theorymentioning

confidence: 94%

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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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Section: Selmer Groups and Principal Divisorscontrasting

confidence: 99%

Section: MCsupporting

confidence: 55%

Section: Main Results In Higher Codimension Iwasawa Theorymentioning

confidence: 63%

Section: Pseudo-nullity Conjectures In Iwasawa Theorymentioning

confidence: 94%

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

Lei

Palvannan

2019

Preprint

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“…First, we remark that though we have restricted ourselves to classical Iwasawa modules, we expect that the approach we have outlined in this paper will apply to general Selmer groups. This is already illustrated in the recent work of Lei and Palvannan on Selmer groups of supersingular elliptic curves [10].…”

Section: Introductionmentioning

confidence: 68%

Exterior powers in Iwasawa theory

Bleher,

Chinburg,

Greenberg

et al. 2019

Preprint

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The Iwasawa theory of CM fields has traditionally concerned Iwasawa modules that are abelian pro-p Galois groups with ramification allowed at a maximal set of primes over p such that the module is torsion. A main conjecture for such an Iwasawa module describes its codimension one support in terms of a p-adic L-function attached to the primes of ramification.In this paper, we study more general and potentially much smaller Iwasawa modules that are quotients of exterior powers of Iwasawa modules with ramification at a set of primes over p by sums of exterior powers of inertia subgroups. We show that the higher codimension support of such quotients can be measured by finite collections of characteristic ideals of classical Iwasawa modules, hence by p-adic L-functions under the relevant CM main conjectures.

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On the growth of Mordell–Weil ranks in $p$-adic Lie extensions

Hung

Lim

2020

Asian Journal of Mathematics

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Codimension two cycles in Iwasawa theory and elliptic curves with supersingular reduction

Cited by 3 publications

References 31 publications

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

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

Exterior powers in Iwasawa theory

On the growth of Mordell–Weil ranks in $p$-adic Lie extensions

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