Alberto F. Boix

An algorithm for producing F-pure ideals

This paper describes a method for computing all F-pure ideals for a given Cartier map of a polynomial ring over a finite field.

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.

On Some Local Cohomology Spectral Sequences

We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain applying a family of functors to a single module. For the second type we follow a completely different strategy as we start with the inverse system that we obtain by applying a covariant functor to an inverse system. The spectral sequences involve the right derived functors of the corresponding limit. We also have a version for contravariant functors. In all the introduced spectral sequences we provide sufficient conditions to ensure their degeneration at their second page. As a consequence we obtain some decomposition theorems that greatly generalize the well-known decomposition formula for local cohomology modules given by Hochster.

Differential operators and hyperelliptic curves over finite fields

Boix, De Stefani and Vanzo have characterized ordinary/supersingular elliptic curves over

Frobenius and Cartier algebras of Stanley–Reisner rings

\mathbb{F}_p

The TestIdeals package for Macaulay2.

in terms of the level of the defining cubic homogenous polynomial. We extend their study to arbitrary genus, in particular we prove that every ordinary hyperelliptic curve

Correction to: Annihilators of local cohomology modules and simplicity of rings of differential operators

\mathcal{C}

Revisiting the determinacy on New Keynesian Models

of genus

Koszul complex over skew polynomial rings

g\geq 2

An algorithm for constructing certain differential operators in positive characteristic

has level