On the structure of the graded algebra associated to a valuation

Autor(es)

Barnabe, M. S. ^[1] ; Novacoski, J. ^[1] ; Spivakovsky, M. ^{[2, 3, 4]}

Afiliação do(s) autor(es)

^[1] Dept Matemat UFSCar, Rodovia Washington Luis 235, BR-13565905 Sao Carlos, SP - Brazil

^[2] CNRS, UMR 5219, 118 Rte Narbonne, F-31062 Toulouse 9 - France

^[3] Inst Math Toulouse, 118 Rte Narbonne, F-31062 Toulouse 9 - France

^[4] Univ Nacl Autonoma Mexico, CNRS, UMI 2001, Inst Matemat, Unidad Cuernavaca LaSol, Av Univ S-N Col Lomas Chamilpa, Cuernavaca 62210, Morelos - Mexico

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 560, p. 667-679, OCT 15 2020.
• Citações Web of Science: 0

Resumo

The main goal of this paper is to study the structure of the graded algebra associated to a valuation. More specifically, we prove that the associated graded algebra gr(v) (R) of a subring (R, m) of a valuation ring O-v, for which Kv := O-v/m(v) = R/m, is isomorphic to Kv {[}t(v(R))], where the multiplication is given by a twisting. We show that this twisted multiplication can be chosen to be the usual one in the cases where the value group is free or the residue field is closed by radicals. We also present an example that shows that the isomorphism (with the trivial twisting) does not have to exist. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 17/17835-9 - As relações entre geometria tórica, teoria de blow-ups locais e teoria de ramificação e suas applicações em teoria das valorizações
• Beneficiário: Josnei Antonio Novacoski
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores