Séminaire d'algèbre et de géométrie du 01-07-2024

Exposé de Nico Lorenz

Le 01-07-2024 à 14:00, en P108 et en ligne.

Isotropy Indices of Pfister multiples in Characteristic 2

Résumé

Let ϕ be a quadratic form and π be a bilinear Pfister form over some field F of characteristic 2. Given a further quadratic form ψ, we compare the isotropy behaviour of ϕ over the function field F(ψ) with the isotropy behaviour of π ⨂ ϕ over F(π ⨂ ψ). In particular, when ψ=ϕ, we investigate the first isotropy index of these forms and show the inequality i₁(π ⨂ ϕ) ≧ i₁(ϕ) … dim(π). We finally discuss situations in which equality and strict inequality hold.