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Iwasawa theory for Rankin-Selberg products of p-non-ordinary eigenforms
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Buyukboduk, Kazim, Lei, Antonio, Loeffler, David and Venkat, Guhan (2019) Iwasawa theory for Rankin-Selberg products of p-non-ordinary eigenforms. Algebra & Number Theory, 13 (4). pp. 901-941. doi:10.2140/ant.2019.13.901 ISSN 1937-0652.
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Official URL: http://dx.doi.org/10.2140/ant.2019.13.901
Abstract
Let f and g be two modular forms which are non-ordinary at p. The theory of Beilinson-Flach elements gives rise to four rank-one non-integral Euler systems for the Rankin-Selberg convolution f⊗g, one for each choice of p-stabilisations of f and g. We prove (modulo a hypothesis on non-vanishing of p-adic L-fuctions) that the p-parts of these four objects arise as the images under appropriate projection maps of a single class in the wedge square of Iwasawa cohomology, confirming a conjecture of Lei-Loeffler-Zerbes.
Furthermore, we define an explicit logarithmic matrix using the theory of Wach modules, and show that this describes the growth of the Euler systems and p-adic L-functions associated to f⊗g in the cyclotomic tower. This allows us to formulate "signed" Iwasawa main conjectures for f⊗g in the spirit of Kobayashi's ±-Iwasawa theory for supersingular elliptic curves; and we prove one inclusion in these conjectures under our running hypotheses.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Algebra & Number Theory | ||||||
Publisher: | Mathematical Sciences Publishers | ||||||
ISSN: | 1937-0652 | ||||||
Official Date: | 6 May 2019 | ||||||
Dates: |
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Volume: | 13 | ||||||
Number: | 4 | ||||||
Page Range: | pp. 901-941 | ||||||
DOI: | 10.2140/ant.2019.13.901 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 12 February 2019 | ||||||
Date of first compliant Open Access: | 20 May 2019 | ||||||
Related URLs: | |||||||
Open Access Version: |
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