Resumen de Bernstein-Sato theory for linearly square-free polynomials in positive characteristic

Pedro López Sancha

• català

  La teoria de Bernstein–Sato ha esdevingut recentment un tema central a l’àlgebra commutativa i la geometria algebraica, atès que constitueix una poderosa eina per a classificar i quantificar singularitats en varietats algebraiques. En particular, ha sorgit un gran interès per estendre la teoria a anells de característica positiva. En aquest article, considerem una classe de polinomis, que denominem polinomis linealment lliures de quadrats, i investiguem els seus invariants associats en el context de la teoria de Bernstein–Sato.

• English

  Bernstein–Sato theory has recently emerged as a central topic in commutative algebra and algebraic geometry, as it constitutes a powerful tool in classifying and quantifying singularities of algebraic varieties. Notably, there has been a surge of interest in extending this theory to the positive characteristic setting. In this work, we consider a class of polynomials, which we call linearly square-free polynomials, and investigate their associated invariants within the context of Bernstein–Sato theory.