Valuations on K[x] approaching a fixed irreducible polynomial

Autor(es)

Barnabe, Matheus dos Santos ^[1] ; Novacoski, Josnei ^[1]

Afiliação do(s) autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 592, p. 100-117, FEB 15 2022.
• Citações Web of Science: 0

Resumo

For a fixed irreducible polynomial F we study the set nu(F) of all valuations on K {[}x] bounded by valuations whose support is (F). The first main result presents a characterization for valuations in nu(F) in terms of their graded rings. We also present a result which gives, for a fixed nu is an element of nu(F) and a key polynomial Q is an element of KP(nu), the maximum value that augmented valuations in nu(F) can assume on Q. This value is presented explicitly in terms of the slopes of the Newton polygon of F with respect to Q. Finally, we present some results about Artin-Schreier extensions that illustrate the applications that we have in mind for the results in this paper. (C) 2021 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