The defect formula

Author(s)

Nart, Enric ; Novacoski, Josnei

• Document type: Journal article
• Source: ADVANCES IN MATHEMATICS; v. 428, p. 44-pg., 2023-06-12.

Abstract

In this paper we present a characterization for the defect of simple algebraic extensions of valued fields. This character-ization generalizes the known result for the henselian case, namely that the defect is the product of the relative degrees of limit augmentations. The main tool used here is the graded algebra associated to a valuation on a polynomial ring. Let Kh be a henselization of a valued field K. Another relevant result proved in this paper is that for every valuation & mu;h on Kh[x], with restriction & mu; on K[x], the corresponding map G & mu; G & mu;h of graded algebras is an isomorphism. & COPY; 2023 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 21/11246-7 - Advances in the problem of local uniformization in positive characteristic
• Grantee: Josnei Antonio Novacoski
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 17/17835-9 - The relation between toric geometry, theory of local blow-ups and ramification theory and their applications in valuation theory
• Grantee: Josnei Antonio Novacoski
• Support Opportunities: Research Grants - Young Investigators Grants