Capítulos (Álgebra)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10805

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Mostrando 1 - 13 de 13

Extending valuations to formal completions
(2014-09-01) Herrera Govantes, Francisco Javier; Olalla Acosta, Miguel Ángel; Spivakovsky, Mark; Teissier, Bernard; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
This paper is an extended version of the talk given by Miguel Angel Olalla Ácosta at the International Conference on Valuation Theory in El Escorial in July 2011. Its purpose is to provide an introduction to our joint paper [5] without grinding through all of its technical details. We refer the reader to [5] for details and proofs; only a few proofs are given in the present paper.
La Teoría Algebraica de los Sistemas Diferenciales Lineales
(Editorial Universidad de Sevilla, 2013) Narváez Macarro, Luis; Álgebra; Briales Morales, Emilio; Chacón Rebollo, Tomás; Carriazo Rubio, Alfonso; Real Jurado, Pedro; Romero Jiménez, Álvaro; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
En estas notas se hace un recorrido por la Teoríaa Algebraica de los Sistemas Diferenciales Lineales, insistiendo en sus motivaciones, en sus nociones y resultados básicos y en sus aportaciones e interacciones con otros campos de las Matemáticas.
Le théorème de constructibilité de Kashiwara
(Hermann, 1993) Mebkhout, Zoghman; Narváez Macarro, Luis; Álgebra; Maisonobe, Philippe; Sabbah, Claude; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Division Theorem over the Dwork-Monsky-Washnitzer Completion of Polynomial Rings and Weyl Algebras
(1998) Narváez Macarro, Luis; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
This chapter provides proofs of Weierstrass-Hironaka division theorems for the Dwork-Monsky-Washnitzer completion of polynomial and Weyl algebras in several variables with coefficients in a complete discrete valuation ring. The case of polynomial algebras generalizes the Weierstrass division theorem and precises the original proof of noetherianity. The case of Weyl algebras is considered in order to analyze division techniques over the ring of infinite linear differential operators and over a smooth weakly formal scheme. A proof in the case of the full completion of Weyl algebras in one variable is proposed independently. The chapter also discusses rings of Dwork-Monsky-Washnitzer power series, division over polynomial rings with coefficients in a field, and division over strictly convergent or power series rings.
On K1 of a Waldhausen category
(EMS Press, 2008-10-06) Muro Jiménez, Fernando; Tonks, Andrew; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
We give a simple representation of all elements in K1 of a Waldhausen category and prove relations between these representatives which hold in K1.
Uso del aprendizaje basado en preguntas en geometría
(Universidad de Sevilla, 2021) Gago Vargas, Manuel Jesús; Álgebra
Propuesta de acciones concretas para superar el sesgo de género en el primer año de formación universitaria en Matemáticas
(Dykinson, 2022) Cumplido Cabello, María; Álgebra; Aránguez Sánchez, Tasia; Olariu, Ozana; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Los algoritmos de las redes sociales y el debate feminista
(Dykinson, 2021) Cumplido Cabello, María; Álgebra; Aránguez Sánchez, Tasia; Olariu, Ozana; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
Hasse–Schmidt derivations versus classical derivations
(American Mathematical Society, 2020-01-17) Narváez Macarro, Luis; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
In this paper we survey the notion and basic results on multivariate Hasse–Schmidt derivations over arbitrary commutative algebras and we associate to such an object a family of classical derivations. We study the behavior of these derivations under the action of substitution maps and we prove that, in characteristic 0, the original multivariate Hasse–Schmidt derivation can be recovered from the associated family of classical derivations. Our constructions generalize a previous one by M. Mirzavaziri in the case of a base field of characteristic 0.
On Hasse–Schmidt Derivations: The Action of Substitution Maps
(Springer, 2018-09-19) Narváez Macarro, Luis; Álgebra; FQM218: Singularidades, Geometría Algebraica Aritmética, Grupos y Homotopía
We study the action of substitution maps between power series rings as an additional algebraic structure on the groups of Hasse–Schmidt derivations. This structure appears as a counterpart of the module structure on classical derivations.
La Geometría Algebraica: punto de encuentro de las Matemáticas
(Real Academia Sevillana de Ciencias, 2005) Narváez Macarro, Luis; Álgebra; FQM218: Geometría Algebraica, Sistemas Diferenciales y Singularidades
Galois representations and Galois groups over Q
(Springer, 2015) Arias de Reyna Domínguez, Sara; Armana, Cécile; Karemaker, Valentijn; Rebolledo, Marusia; Thomas, Lara; Vila Oliva, Núria; Álgebra; Bertin, Marie José; Bucur, Alina; Feigon, Brooke; Schneps, Leila; FQM218: Geometría Algebraica, Sistemas Diferenciales y Singularidades
In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve, let J(C) be the associated Jacobian variety and let ¯ρℓ : GQ → GSp(J(C)[ℓ]) be the Galois representation attached to the ℓ-torsion of J(C). Assume that there exists a prime p such that J(C) has semistable reduction with toric dimension 1 at p. We provide an algorithm to compute a list of primes ℓ (if they exist) such that ¯ρℓ is surjective. In particular we realize GSp6 (Fℓ) as a Galois group over Q for all primes ℓ ∈ [11, 500000].
Computer algebra and algebraic analysis
(Universidad de La Rioja, 2010) Castro Jiménez, Francisco Jesús; Álgebra; Lambán Pardo, Laureano; Romero Ibáñez, Ana; Rubio García, Julio; FQM333: Álgebra Computacional en Anillos no Conmutativos y Aplicaciones
Este artículo describe algunas aplicaciones del Álgebra Computacional al Análisis Algebraico, también conocido como teoría de D-módulos, es decir, el estudio algebraico de sistemas lineales de ecuaciones en derivadas parciales. Mostramos cómo calcular diferentes objetos e invariantes en teoría de D-módulos, utilizando bases de Groebner para anillos de operadores diferenciales lineales.

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