A henselian preparation theorem

Laurent Moret-Bailly (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We prove an analogue of the Weierstrass preparation theorem for henselian pairs, generalizing the local case recently proved by Bouthier and Česnavičius. As an application, we construct a henselian analogue of the resultant of p-adic series defined by Berger.

Mots clés: AMS 2020 Classification: 13J15; 13B40; 13P15; henselian pair; Weierstrass preparation theorem; resultant

Domaines: Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]

Laurent Moret-Bailly. A henselian preparation theorem. Israel Journal of Mathematics, 2023, 257, pp.519-531. ⟨10.1007/s11856-023-2545-1⟩. ⟨hal-03502426v4⟩