Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On analogues of Mazur-Tate type conjectures in the Rankin-Selberg
  setting   We study the Fitting ideals over the finite layers of the cyclotomic
$\mathbb{Z}_p$-extension of $\mathbb{Q}$ 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 ``Refined
conjectures of the Birch and Swinnerton-Dyer type'', 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 \emph{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 $\rho$ with
splitting field $F$. As an application, we give an upper bound of the dimension
of the $\rho$-isotypic component of the Mordell-Weil group of $E$ over the
finite layers of the cyclotomic $\mathbb{Z}_p$-extension of $F$ in terms of the
order of vanishing of our Theta elements.

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The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas