A localized version of the basic triangle theorem

Gérard Duchamp (1) , Nihar P Gargava (2) , Hoang Ngoc Minh (1) , Pierre Simonnet (3)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 EPFL - Ecole Polytechnique Fédérale de Lausanne
3 SPE - Sciences pour l'environnement

In this short note, we give a localized version of the basic triangle theorem, first published in 2011 (see [4]) in order to prove the independence of hyperlogarithms over various function fields. This version provides direct access to rings of scalars and avoids the recourse to fraction fields as that of meromorphic functions for instance.

Domaines: Calcul formel [cs.SC]; Combinatoire [math.CO]; Algèbre commutative [math.AC]

Gérard Duchamp, Nihar P Gargava, Hoang Ngoc Minh, Pierre Simonnet. A localized version of the basic triangle theorem. 2020. ⟨hal-02264912v3⟩