43 citations · 58 across the 19 of their papers we have counts for
28 papers
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
Let be an excellent local noetherian domain with field of fractions . Let be a valuation centered at and let be the correspondi…
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 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…
Cusps of caustics by reflection in ellipses
Gil Bor, Mark Spivakovsky, Serge Tabachnikov
This paper is concerned with the billiard version of Jacobi's last geometric statement and its generalizations. Given a non-focal point inside an elliptic billiard table, one c…
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…