Iwasawa theory for Rankin-Selberg products ofp-nonordinary eigenforms
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Bibliographic record
Abstract
Let [math] and [math] be two modular forms which are nonordinary at [math] . The theory of Beilinson–Flach elements gives rise to four rank-one nonintegral Euler systems for the Rankin–Selberg convolution [math] , one for each choice of [math] -stabilisations of [math] and [math] . We prove (modulo a hypothesis on nonvanishing of [math] -adic [math] -functions) that the [math] -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.\n¶ 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 [math] -adic [math] -functions associated to [math] in the cyclotomic tower. This allows us to formulate “signed” Iwasawa main conjectures for [math] in the spirit of Kobayashi’s [math] -Iwasawa theory for supersingular elliptic curves; and we prove one inclusion in these conjectures under our running hypotheses.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.025 | 0.006 |
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