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pro vyhledávání: '"Cauchi, Antonio"'
Let $E/F$ be a quadratic extension of totally real number fields. We show that the generalized Hirzebruch-Zagier cycles arising from the associated Hilbert modular varieties can be put in $p$-adic families. As an application, using the theory of base
Externí odkaz:
http://arxiv.org/abs/2411.02984
We give a two-variable Rankin--Selberg integral for generic cusp forms on $\mathrm{PGL}_4$ and $\mathrm{PGU}_{2,2}$ which represents a product of exterior square $L$-functions. As a residue of our integral, we obtain an integral representation on $\m
Externí odkaz:
http://arxiv.org/abs/2402.09855
We study Shalika models for generic unramified representations of $\mathrm{PGU}_{2,2}$ over non-archimedean local fields. We prove that they always exist and show that they are in fact unique up to constant by means of the theta correspondence for $(
Externí odkaz:
http://arxiv.org/abs/2311.05759
We provide a new description of Deligne-Beilinson cohomology for any Shimura variety in terms of tempered currents. This is particularly useful for computations of regulators of motivic classes and hence to the study of Beilinson conjectures. As an a
Externí odkaz:
http://arxiv.org/abs/2204.05163
We study instances of Beilinson-Tate conjectures for automorphic representations of $\mathrm{PGSp}_6$ whose Spin $L$-function has a pole at $s=1$. We construct algebraic cycles of codimension three in the Siegel-Shimura variety of dimension six and w
Externí odkaz:
http://arxiv.org/abs/2202.09394
Autor:
Cauchi, Antonio, Lei, Antonio
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 fo
Externí odkaz:
http://arxiv.org/abs/2005.12105
Akademický článek
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Autor:
Cauchi, Antonio
The main theme of this thesis is on the push-forward construction of motivic cohomology classes for Shimura varieties. This strategy was successfully employed in work of Lei-Loeffler-Zerbes et al to construct new Euler systems for Galois representati
Externí odkaz:
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.756329
We construct classes in the middle degree plus one motivic cohomology of the Siegel Shimura variety of almost any dimension. We compute their image by Beilinson's higher regulator in terms of Rankin-Selberg type automorphic integrals. Our constructio
Externí odkaz:
http://arxiv.org/abs/1910.11207
We construct global cohomology classes in the middle degree cohomology of the Shimura variety of the symplectic group $GSp_6$ compatible when one varies the level at $p$. These classes are expected constituents of an Euler system for the Galois repre
Externí odkaz:
http://arxiv.org/abs/1807.06512