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Limits of quotients of polynomial functions of three variables, Classification of G-graded twisted algebras and the computation of the F-rational locus

Hernández Rodas, Juan Pablo (2015) Limits of quotients of polynomial functions of three variables, Classification of G-graded twisted algebras and the computation of the F-rational locus. Doctorado thesis, Universidad Nacional de Colombia - Sede Medellín.

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This thesis is divided in three main parts. In the first part we provide a theoretical method to determine the existence of the limit of a quotient of polynomial functions of three variables. An algorithm to compute such limits in the case where the polynomials have rational coeffcients, or more generally, coefficients in a real finite extension of the rational numbers is also described. In the second part, for any finite abelian group G, we present an exact formula to count the G graded twisted algebras satisfying certain symmetry condition. Finally, in the third part we describe an algorithm to compute the F-rational locus of an affine algebra over a field of prime characteristic p > 0 by computing first its global test ideal. As a consequence we deduce the Openness of the F-rational locus, a result originally proved in [27]

Tipo de documento:Tesis/trabajos de grado - Thesis (Doctorado)
Colaborador / Asesor:Vélez Caicedo, Juan Diego
Palabras clave:G-graded twisted algebras, Limits of rational functions of three varibles, F-rational locus
Temática:5 Ciencias naturales y matemáticas / Science > 51 Matemáticas / Mathematics
Unidad administrativa:Sede Medellín > Facultad de Ciencias > Escuela de Matemáticas
Código ID:50191
Enviado por : Sr Juan Pablo Hernández Rodas
Enviado el día :21 Julio 2015 16:41
Ultima modificación:26 May 2018 18:52
Ultima modificación:26 May 2018 18:52
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