Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Salazar, Daniel Barrera"'
Let $\mathcal{C}$ be a hyperelliptic curve $y^2 = p(x)$ defined over a number field $K$ with $p(x)$ integral of odd degree. The purpose of the present article is to prove lower and upper bounds for the $2$-Selmer group of the Jacobian of $\mathcal{C}
Externí odkaz:
http://arxiv.org/abs/2308.08663
Friedberg--Jacquet proved that if $\pi$ is a cuspidal automorphic representation of $\mathrm{GL}_{2n}(\mathbb{A})$, $\pi$ is a functorial transfer from $\mathrm{GSpin}_{2n+1}$ if and only if a global zeta integral $Z_H$ over $H = \mathrm{GL}_n \times
Externí odkaz:
http://arxiv.org/abs/2308.02649
In this paper, we prove that a $\mathrm{GL}(2n)$-eigenvariety is \'etale over the (pure) weight space at non-critical Shalika points, and construct multi-variable $p$-adic $L$-functions varying over the resulting Shalika components. Our constructions
Externí odkaz:
http://arxiv.org/abs/2211.08126
Publikováno v:
J. Th\'eor. Nomb. Bordeaux, 33 (2021), no.3, pp.659-701
The use of overconvergent cohomology in constructing $p$-adic $L$-functions, initiated by Stevens and Pollack--Stevens in the setting of classical modular forms, has now been established in a number of settings. The method is compatible with construc
Externí odkaz:
http://arxiv.org/abs/2108.09191
In this paper, we propose and explore a new connection in the study of $p$-adic $L$-functions and eigenvarieties. We use it to prove results on the geometry of the cuspidal eigenvariety for $\mathrm{GL}_{2n}$ over a totally real number field $F$ at c
Externí odkaz:
http://arxiv.org/abs/2103.10907
Publikováno v:
Math. Z., 299 (2021), no.1, pp.961-995
Let $G'$ be a connected reductive group over $\mathbb{Q}$ such that $G = G'/\mathbb{Q}_p$ is quasi-split, and let $Q \subset G$ be a parabolic subgroup. We introduce parahoric overconvergent cohomology groups with respect to $Q$, and prove a classica
Externí odkaz:
http://arxiv.org/abs/2007.11334
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:
http://arxiv.org/abs/2001.02263
Let F be a totally real number field. Using a recent geometric approach developed by Andreatta and Iovita we construct several variables p-adic families of finite slope quaternionic automorphic forms over F. It is achieved by interpolating the modula
Externí odkaz:
http://arxiv.org/abs/1908.00091
Publikováno v:
Selecta Math., 27 (2021), no.82, pp. 1-45
Let $K$ be an imaginary quadratic field. In this article, we study the eigenvariety for $\mathrm{GL}_2/K$, proving an \'etaleness result for the weight map at non-critical classical points and a smoothness result at base-change classical points. We g
Externí odkaz:
http://arxiv.org/abs/1808.09750
Publikováno v:
Trans. Amer. Math. Soc. 372 (2019), 1-34
Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over an imaginary quadratic field F. In this paper, we prove an exceptional zero conjecture in the case where f is new at a prime above p. More precisely, for each prime $\mathfr
Externí odkaz:
http://arxiv.org/abs/1707.04049