2021
DOI: 10.48550/arxiv.2109.08375
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Iwasawa-Greenberg main conjecture for non-ordinary modular forms and Eisenstein congruences on $\mathrm{GU}(3,1)$

Abstract: In this paper we prove one side divisibility of the Iwasawa-Greenberg main conjecture for Rankin-Selberg product of a weight two cusp form and an ordinary CM form of higher weight, using congruences between Klingen Eisenstein series and cusp forms on GU(3, 1), generalizing earlier result of the third-named author to allow non-ordinary cusp forms. The main result is a key input in the third author's proof for Kobayashi's ±-main conjecture for supersingular elliptic curves. The new ingredient here is developing … Show more

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“…The reverse inclusion of (2.2) has been established in the monumental work of Skinner and Urban [26] for a p-ordinary modular form (under certain hypotheses; see [26,Theorem 1]). In the nonordinary form, there have been several recent breakthroughs in this reverse direction (see [5,6,9]). Finally, the work [16] has supplied many sufficient conditions for the nonvanishing of L p and L p (see [16,Corollary 3.29 and Proposition 3.39]).…”
Section: Definitions Of Selmer Groups and Related Objectsmentioning
confidence: 99%
“…The reverse inclusion of (2.2) has been established in the monumental work of Skinner and Urban [26] for a p-ordinary modular form (under certain hypotheses; see [26,Theorem 1]). In the nonordinary form, there have been several recent breakthroughs in this reverse direction (see [5,6,9]). Finally, the work [16] has supplied many sufficient conditions for the nonvanishing of L p and L p (see [16,Corollary 3.29 and Proposition 3.39]).…”
Section: Definitions Of Selmer Groups and Related Objectsmentioning
confidence: 99%