Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Villegas, Fernando Rodríguez"'
Let $C$ be a genus $2$ curve with Jacobian isomorphic to the square of an elliptic curve with complex multiplication by a maximal order in an imaginary quadratic field of discriminant $-d<0$. We show that if the stable model of $C$ has bad reduction
Externí odkaz:
http://arxiv.org/abs/2412.08738
We consider all irreducible rank-4 hypergeometric local systems defined over $\mathbb{Q}$ that support a rational one-dimensional variation of Hodge structures of weight 3 and Hodge vector $(1,1,1,1)$. Up to a natural equivalence there are only 47 ca
Externí odkaz:
http://arxiv.org/abs/2401.13529
We give two constructions of families of elliptic curves over cubic or quartic fields with three, respectively four, `integral' elements in the kernel of the tame symbol on the curves. The fields are in general non-Abelian, and the elements linearly
Externí odkaz:
http://arxiv.org/abs/2401.04510
We study a hypergeometric local system that arises from the quantum Chen-Ruan cohomology of a family of weighted del Pezzo hypersurfaces. We prove that it is the anti-invariant variation of a pencil of genus-7 curves with respect to an involution hav
Externí odkaz:
http://arxiv.org/abs/2210.14344
Survey of hypergeometric motives, with a focus on their source varieties, Hodge numbers, and L-functions.
Externí odkaz:
http://arxiv.org/abs/2109.00027
Let $\Gamma$ be a simple graph and $I_\Gamma(x)$ its multivariate independence polynomial. The main result of this paper is the characterization of chordal graphs as the only $\Gamma$ for which the power series expansion of $I_\Gamma^{-1}(x)$ is Horn
Externí odkaz:
http://arxiv.org/abs/1908.11231
Autor:
Villegas, Fernando Rodriguez
This note is an extended version of the slides for my talk with the same title at the {\it Arithmetic, geometry, and modular forms: a conference in honour of Bill Duke} in June 2019 at the ETH in Z"urich. The results presented concern three geometric
Externí odkaz:
http://arxiv.org/abs/1907.02722
In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra R by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely indecomposable
Externí odkaz:
http://arxiv.org/abs/1810.01818
We discuss two related principles for hypergeometric supercongrences, one related to accelerated convergence and the other to the vanishing of Hodge numbers. This is an extended abstract of a talk given at the workshop "Hypergeometric motives and Cal
Externí odkaz:
http://arxiv.org/abs/1803.10834
Autor:
Villegas, Fernando Rodriguez
We study classical hypergeometric series as a p-adic function of its parameters inspired by a problem in the American Mathematical Monthly solved by D. Zagier. This is an extended abstract of a talk given at the workshop "Hypergeometric motives and C
Externí odkaz:
http://arxiv.org/abs/1803.10802