The Weierstrass preparation theorem and resultants of $p$-adic power series

Laurent Berger (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

We define the resultant of two power series with coefficients in the ring of integers of a $p$-adic field. In order to do this, we prove a universal version of the Weierstrass preparation theorem.

Domaines: Théorie des nombres [math.NT]

Laurent Berger. The Weierstrass preparation theorem and resultants of $p$-adic power series. Münster Journal of Mathematics, 2021, 14, pp.155--163. ⟨hal-02314879⟩