On analogues of Mazur-Tate type conjectures in the Rankin-Selberg setting
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Bibliographic record
Abstract
We study the Fitting ideals over the finite layers of the cyclotomic Zp-extension of Q of Selmer groups attached to the Rankin-Selberg convolution of two modular forms f and g. Inspired by the theta elements for modular forms defined by Mazur and Tate in [32], we define new theta elements for Rankin-Selberg convolutions of f and g using Loeffler-Zerbes' geometric p-adic L-functions attached to f and g. Under certain technical hypotheses, we generalize a recent work of Kim-Kurihara on elliptic curves to prove a result very close to the weak main conjecture of Mazur and Tate for Rankin-Selberg convolutions. Special emphasis is given to the case where f corresponds to an elliptic curve E and g to a two-dimensional odd irreducible Artin representation ρ with splitting field F. As an application, we give an upper bound of the dimension of the ρ-isotypic component of the Mordell-Weil group of E over the finite layers of the cyclotomic Zp-extension of F in terms of the order of vanishing of our theta elements.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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