Sums of squares in function fields over Henselian local fields - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematische Annalen Année : 2019

Sums of squares in function fields over Henselian local fields

Résumé

We give upper bounds for the level and the Pythagoras number of function fields over fraction fields of integral Henselian excellent local rings. In particular, we show that the Pythagoras number of $\mathbb{R}((x_1,\dots,x_n))$ is $\leq 2^{n-1}$, which answers positively a question of Choi, Dai, Lam and Reznick.

Dates et versions

hal-02353159 , version 1 (07-11-2019)

Identifiants

Citer

Olivier Benoist. Sums of squares in function fields over Henselian local fields. Mathematische Annalen, 2019, 376 (1), pp.683-692. ⟨10.1007/s00208-019-01935-z⟩. ⟨hal-02353159⟩
30 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More