272 research outputs found
Vanishing of local cohomology and set-theoretically Cohen–Macaulay ideals
No full textIn this paper, first, we generalize a result of Peskine–Szpiro on the relation between the cohomological dimension and projective dimension. Then, we give conditions for the vanishing of local cohomology from local to global and vice versa. Our final goal in the present paper is to examine the set-theoretically Cohen–Macaulay ideals to find some cohomological characterization of these kinds of ideals.A. F. Boix was partially supported by the Spanish Ministry of Science and Innovation Grant PID2019–104844GB–I00.Peer ReviewedPreprin
An algorithm for constructing certain differential operators in positive characteristic
No full textGiven 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 pth 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.<br /
Frobenius algebras of rings of prime characteristic: a quick tour
No full textThe goal of this survey is to review several recent results concerning the so–called Frobenius algebras of rings of prime characteristic, focusing specially on the interesting issue of its finite or infinite generation. We specially draw our attention to the case where our base ring is Stanley–Reisner, where explicit and algorithmic descriptions of these algebras are known.Alberto F. Boix is partially supported by Spanish Ministerio de Economía y Competitividad grant PID2022-137283NB-C22.Peer ReviewedPostprint (published version
Frobenius algebras of rings of prime characteristic: a quick tour
No full textThe goal of this survey is to review several recent results concerning the so–called Frobenius algebras of rings of prime characteristic, focusing specially on the interesting issue of its finite or infinite generation. We specially draw our attention to the case where our base ring is Stanley–Reisner, where explicit and algorithmic descriptions of these algebras are known.Alberto F. Boix is partially supported by Spanish Ministerio de Economía y Competitividad grant PID2022-137283NB-C22.Peer ReviewedPostprint (published version
MacWilliams duality for rank metric codes over finite chain rings
No full textWe extend Ravagnani's MacWilliams duality theory to the setting of rank metric codes over finite chain rings, relating the sequences of q-binomial moments of a rank metric code over this class of rings with those of its dual.I. Blanco-Chacón and M. Greferath are partially supported by the Research Council of Finland (project #351271, PI Camilla Hollanti). I. Blanco-Chacón is also partially supported by Spanish Ministerio de Ciencia e Innovación grant PID2022-136944NB-I00. E. Hieta-aho was partially supported by Research Council of Finland, grant #336005 (PI Camilla Hollanti). A. F. Boix is partially supported by Spanish Ministerio de Ciencia e Innovación grant PID2022-137283NB-C22.Peer ReviewedPostprint (published version
Identification and mitigation of sinkhole hazards in an evaporite karst area (Perdiguera, Spain)
No full text[EN] Sinkhole risks are becoming particularly severe in urban areas that lack careful planning and where karst depressions are frequently filled and developed. Sinkholes frequently have a higher probability of occurrence and a bigger genetic diversity in evaporite rocks than in carbonate rocks. This is because evaporites rocks (halite, gypsum, etc) have a higher solubility. Subsidence damage resulting from this dissolution generates considerable losses at the world. To contract with these risks, is needed the identification, investigation, prediction, and mitigation of sinkholes. Corrective measures might be applied to reduce the subsidence processes. A more practical solution for safe development is to reduce the vulnerability of the structures by using subsidence-proof designs. Therefore, this case study is located in the town of Perdiguera (Zaragoza, Spain), within the Ebro Basin. This town is affected by subsidence problems, which are associated with the dissolution of gypsiferous silts that generate sinking. These sinkholes are affecting the buildings threatening its structural integrity.The authors of this article would like to thank the Ibergeotecnia, S.R.L. for providing the initial data. Also, thanks to María Estefanía Bona, MSc and Jesús Juan Usón for their contribution on this article. This paper is related with the research project "RISK-Terra. Earthen architecture in the Iberian Peninsula: study of natural, social and anthropic risks and strategies to improve resilience" (RTI2018-095302-B-I00), funded by the Spanish Ministry of Science, Innovation and Universities.Torrijo, F.; Fuentes, R.; Boix, A.; Brachhi, P. (2020). Identification and mitigation of sinkhole hazards in an evaporite karst area (Perdiguera, Spain). International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences (Online). XLIV-M-1:707-712. https://doi.org/10.5194/isprs-archives-XLIV-M-1-2020-707-2020S707712XLIV-M-
Certain endomorphism rings of local cohomology modules and Lyubeznik numbers
No full textThe 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 cohomology fails, leading us to simpler expressions
of certain local cohomology modules. As application, we give new expressions of
the endomorphism ring of these modules. On the other hand, building upon
previous work by \`Alvarez Montaner, we exhibit the shape of Lyubeznik tables
of the so--called partially sequentially Cohen--Macaulay rings as introduced by
Sbarra and Strazzanti.Comment: 13 pages, comments are welcom
On the infinitely generated locus of Frobenius algebras of rings of prime characteristic
No full textThis version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s40306-023-00515-3Let R be a commutative Noetherian ring of prime characteristic p. The main goal of this paper is to study in some detail when {p ¿ Spec(R) : FEp is finitely generated as a ring over its degree zero piece} is an open set in the Zariski topology, where FEp denotes the Frobenius algebra attached to the injective hull of the residue field of Rp. We show that this is true when R is a StanleyReisner ring; moreover, in this case, we explicitly compute its closed complement, providing an algorithmic method for doing so.Alberto F. Boix and S. Zarzuela are partially supported by the Spanish Ministerio de Economía y Competitividad grant PID2019-104844GB-I00.Peer ReviewedPostprint (author's final draft
RESCON: Educational project scheduling software.
No full textIn this article we discuss a freely downloadable educational software tool for illustrating project scheduling and project management concepts. The tool features exact and heuristic scheduling procedures and visualizes project networks, project schedules, resource profiles, activity slacks, and project duration distributions.Project scheduling; Project management; Educational software; Visualization; Scheduling algorithms;
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