Galois representations of superelliptic curves

Autor: Ariel Pacetti, Angel Villanueva

Publikováno v: Glasgow Mathematical Journal. :1-27

A superelliptic curve over a discrete valuation ring $\mathscr{O}$ of residual characteristic p is a curve given by an equation $\mathscr{C}\;:\; y^n=\,f(x)$ , with $\textrm{Disc}(\,f)\neq 0$ . The purpose of this article is to describe the Galois re

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7e0639cea8a5948275deb0193e198c53
https://doi.org/10.1017/s0017089522000386

On $2$-Selmer groups and quadratic twists of elliptic curves

Autor: Daniel Barrera Salazar, Ariel Pacetti, Gonzalo Tornaría

Publikováno v: Mathematical Research Letters. 28:1633-1659

Let $K$ be a number field and $E/K$ be an elliptic curve with no $2$-torsion points. In the present article we give lower and upper bounds for the $2$-Selmer rank of $E$ in terms of the $2$-torsion of a narrow class group of a certain cubic extension

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::341674764d41ded88f9f572cf72fc537
https://doi.org/10.4310/mrl.2021.v28.n6.a1

Modularity of the Consani-Scholten quintic

Autor: Gil, J. B., Dieulefait, L., Ariel Pacetti, Schütt, M.

Publikováno v: Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Scopus-Elsevier
Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona

We prove that the Consani-Scholten quintic, a Calabi-Yau threefold over Q, is Hilbert modular. For this, we refine several techniques known from the context of modular forms. Most notably, we extend the Faltings-Serre-Livn'e method to induced four-di

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::190ba50f06e143f1d4250cbc5b811e34
http://hdl.handle.net/2072/419040

Anticyclotomic p-adic L-functions for elliptic curves at some additive reduction primes

Autor: Ariel Pacetti, Daniel Kohen

Publikováno v: Comptes Rendus Mathematique. 356:973-983

Let $E$ be a rational elliptic curve and let $p$ be an odd prime of additive reduction. Let $K$ be an imaginary quadratic field and fix a positive integer $c$ prime to the conductor of $E$. The main goal of the present article is to define an anticyc

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c2a7bce42434f81bf38a757fe2fe6cff
https://doi.org/10.1016/j.crma.2018.09.005

Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields

Autor: José Ignacio Burgos Gil, Ariel Pacetti

Publikováno v: CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas
instacron:CONICET

In this article we give an analogue of Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields. Let $K$ be a real quadratic field and $\Om_K$ its ring of integers. Let $\Gamma$ be a congruence subgroup of $\SL_2(\Om_K)$ and $M_{(k

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::125e5e0a8428ed17d04911736b896823
https://doi.org/10.1090/mcom/3187