3 papers
math.AC2026
On topologies on the space of valuations and the valuative tree
Vinicius Manfredini, Josnei Novacoski, Caio Henrique Silva de Souza
In this paper, we discuss topological aspects of the space of valuations and the valuative tree . We present a relation between the weak tree topolo…
math.AC2025
On defect in finite extensions of valued fields
Caio Henrique Silva de Souza, Mark Spivakovsky
In recent decades, the defect of finite extensions of valued fields has emerged as the main obstacle in several fundamental problems in algebraic geometry such as the local uniform…
math.AC2025
Tame fields, Graded Rings and Finite Complete Sequences of Key Polynomials
Caio Henrique Silva de Souza
In this paper, we present a criterion for to be henselian and defectless in terms of finite complete sequences of key polynomials. For this, we use the theory of Mac Lane-V…