7 citations · 28 across the 19 of their papers we have counts for
15 papers · 1 filter
When does a derivation of a ring admit the exponential?
Genrich Belitskii, Alberto F. Boix, Dmitry Kerner
Exponentials of (real/complex) vector fields are classically defined via the vector field integration. Take a k-algebra k[x] \subset R\subset k[[x]], where k\supseteq \Q is a local…
Exploring a local variant of the Buchsbaum--Eisenbud--Horrocks conjecture
Alberto F. Boix, Bárbara K. Lima--Pereira
The Buchsbaum--Eisenbud--Horrocks conjecture has attracted the attention of many researchers working in Commutative Algebra and Algebraic Geometry in the last fifty years. Quite re…
Certain endomorphism rings of local cohomology modules and Lyubeznik numbers
Alberto F. Boix, Majid Eghbali
The goal of this paper is twofold; on the one hand, motivated by questions raised by Schenzel, we explore situations where the Hartshorne--Lichtenbaum Vanishing Theorem for local c…
On the infinitely generated locus of Frobenius algebras of rings of prime characteristic
Alberto F. Boix, Danny A. J. Gómez--Ramírez, Santiago Zarzuela
Let be a commutative Noetherian ring of prime characteristic . The main goal of this paper is to study in some detail when \[ \overline{W^R}:=\{\mathfrak{p}\in\operatorname{…
Surjectivity of the completion map for rings of -functions. (Whitney extension theorem for general filtrations)
Genrich Belitskii, Dmitry Kerner
The classical lemma of Borel reads: any power series with real coefficients is the Taylor series of a smooth function. Algebraically this means the surjectivity of the completion m…
Approximation results of Artin-Tougeron-type for general filtrations and for -equations
Genrich Belitskii, Alberto F. Boix, Dmitry Kerner
Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals,…
The level of pairs of polynomials
Alberto F. Boix, Marc Paul Noordman, Jaap Top
Given a polynomial with coefficients in a field of prime characteristic , it is known that there exists a differential operator that raises to its th power. We firs…
The TestIdeals package for Macaulay2
Alberto F. Boix, Daniel J. Hernández, Zhibek Kadyrsizova +7
This note describes a \emph{Macaulay2} package for computations in prime characteristic commutative algebra. This includes Frobenius powers and roots, -linear and -l…
Vanishing of local cohomology and set-theoretically Cohen-Macaulay ideals
Majid Eghbali, Alberto F. Boix
We generalize some known results on the relation between the cohomological and projective dimension. Then we examine the set-theoretically Cohen-Macaulay ideals to find some cohomo…
On some local cohomology spectral sequences
Josep Àlvarez Montaner, Alberto F. Boix, Santiago Zarzuela
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…
Frobenius and Cartier algebras of Stanley-Reisner rings (II)
Alberto F. Boix, Santiago Zarzuela
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…
Annihilators of local cohomology modules and simplicity of rings of differential operators
Alberto F. Boix, Majid Eghbali
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…
An algorithm for constructing certain differential operators in positive characteristic
Alberto F. Boix, Alessandro De Stefani, Davide Vanzo
Given a non-zero polynomial in a polynomial ring with coefficients in a finite field of prime characteristic , we present an algorithm to compute a differential operator…
An algorithm for producing F-pure ideals
Alberto F. Boix, Mordechai Katzman
This paper describes a method for computing all F-pure ideals for a given Cartier map of a polynomial ring over a finite field.
Frobenius and Cartier algebras of Stanley-Reisner rings
Josep Alvarez Montaner, Alberto F. Boix, Santiago Zarzuela
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…