From the 2 of 6 linked papers with an AI index.
20 citations · 20 across the 2 of their papers we have counts for
6 papers
Key polynomials for simple extensions of valued fields
F. J. Herrera Govantes, W. Mahboub, M. A. Olalla Acosta +1
The paper refines MacLane’s theory of key polynomials for simple transcendental extensions of rank‑1 valued fields, explicitly describing limit key polynomials and giving upper bou…
Extending valuations of local domains to complete local domains without changing the value group
F. J. Herrera Govantes, M. A. Olalla Acosta, M. Spivakovsky +1
The paper proves that any valuation on an excellent local Noetherian domain can be extended to its m‑adic completion without changing the value group, confirming Teissier’s conject…
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…
Valuation rings in simple algebraic extensions of valued fields
Josnei Novacoski, Mark Spivakovsky
Consider a simple algebraic valued field extension and denote by and the corresponding valuation rings. The main goal of this paper is to pr…
A note on the Casas-Alvero Conjecture
Daniel Schaub, Mark Spivakovsky
The Casas--Alvero conjecture predicts that every univariate polynomial over a field of characteristic zero having a common factor with each of its derivatives is…
A description of and an upper bound on the set of bad primes in the study of the Casas-Alvero Conjecture
Daniel Schaub, Mark Spivakovsky
The Casas--Alvero conjecture predicts that every univariate polynomial over a field of characteristic zero having a common factor with each of its derivatives is a power o…