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Alberto F. Boix

Publications and source records attributed to Alberto F. Boix.

24 records · Page 2Linked to original sources
arXiv2017

Frobenius and Cartier algebras of Stanley-Reisner rings (II)

It is known that the Frobenius algebra of the injective hull of the residue field of a complete Stanley--Reisner ring (i.e. a formal power series ring modulo a squarefree monomial ideal) can be only principally generated or infinitely generated as algebra over its degree zero piece, and that this fact can be read off in the corresponding simplicial complex; in the infinite case, we exhibit a 1--1 correspondence between potential new generators appearing on each graded piece and certain pairs of faces of such a simplicial complex, and we use it to provide an alternative proof of the fact that these Frobenius algebras can only be either principally generated or infinitely generated.

math.AC↗
arXiv2017

Annihilators of local cohomology modules and simplicity of rings of differential operators

One classical topic in the study of local cohomology is whether the non-vanishing of a specific local cohomology module is equivalent to the vanishing of its annihilator; this has been studied by several authors, including Huneke, Koh, Lyubeznik and Lynch. Motivated by questions raised by Lynch and Zhang, the goal of this paper is to provide some new results about this topic, which provide some partial positive answers to these questions. The main technical tool we exploit is the structure of local cohomology as module over rings of differential operators.

math.AC↗
arXiv2015

An algorithm for constructing certain differential operators in positive characteristic

Given a non-zero polynomial $f$ in a polynomial ring $R$ with coefficients in a finite field of prime characteristic $p$, we present an algorithm to compute a differential operator $δ$ which raises $1/f$ to its $p$th power. For some specific families of polynomials, we also study the level of such a differential operator $δ$, i.e., the least integer $e$ such that $δ$ is $R^{p^e}$-linear. In particular, we obtain a characterization of supersingular elliptic curves in terms of the level of the associated differential operator.

math.AC↗
arXiv2012

Cohomological interpretation of quadratic modular symbols

Bayer and Blanco-Chacón have recently defined quadratic modular symbols for the Shimura curves X(D,N) attached to Eichler orders of level N of an indefinite quaternion rational algebra of discriminant D. In this paper, we give a cohomological interpretation of these quadratic modular symbols. Explicit computations for the homology of some Shimura curves are also provided.

math.NT↗
arXiv2011

Frobenius and Cartier algebras of Stanley-Reisner rings

We prove that the Frobenius algebra of the injective hull of a complete Stanley-Reisner ring as well as its Matlis dual notion of Cartier algebra can be only principally generated or infinitely generated. As a consequence we are able to show that the set of F-jumping numbers of generalized test ideals associated to complete Stanley-Reisner rings form a discrete set.

math.AC↗