7 citations · 28 across the 19 of their papers we have counts for
22 papers
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…
MacWilliams duality for rank metric codes over finite chain rings
Iván Blanco-Chacón, Alberto F. Boix, Marcus Greferath +1
We extend Ravagnani's MacWilliams duality theory to the settings of rank metric codes over finite chain rings, relating the sequences of -binomial moments of a rank metric code…
On some algebraic and geometric extensions of Goldbach's conjecture
Alberto F. Boix, Danny A. J. Gómez-Ramírez
The goal of this paper is to study Goldbach's conjecture for rings of regular functions of affine algebraic varieties over a field. Among our main results, we define the notion of…
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{…
Invariants of limit key polynomials
Maria Alberich-Carramiñana, Alberto F. Boix, Julio Fernández +3
Let be a valuation of arbitrary rank on the polynomial ring with coefficients in a field . We prove comparison theorems between MacLane-Vaquié key polynomials for val…
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…
Pairs of Lie-type and large orbits of group actions on filtered modules. (A characteristic-free approach to finite determinacy.)
Alberto F. Boix, Gert-Martin Greuel, Dmitry Kerner
Finite determinacy for mappings has been classically thoroughly studied in numerous scenarios in the real- and complex-analytic category and in the differentiable case. It means th…
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…
Differential operators and hyperelliptic curves over finite fields
Iván Blanco-Chacón, Alberto F. Boix, Stiofáin Fordham +1
Boix, De Stefani and Vanzo have characterized ordinary/supersingular elliptic curves over in terms of the level of the defining cubic homogenous polynomial. We exten…
Revisiting the determinacy on New Keynesian Models: A survey
Alberto F. Boix, Adrián Segura Moreiras
The goal of this paper is to review some analytic techniques that are potentially useful to shed light on the determinacy question that arises in New Keynesian models as result of…
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.
Cohomological interpretation of quadratic modular symbols
Pilar Bayer, Iván Blanco-Chacón, Alberto F. Boix
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 alg…
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…