On the descent for quadratic and bilinear forms

Ahmed Laghribi and Diksha Mukhija

Mathematische Nachrichten, 2025, vol. 298, issue 6, 2037-2059

Abstract: This paper is devoted to the study of the descent problem in the spirit of conjectures proposed by Kahn in characteristic different from 2. The descent problem seeks conditions under which a K$K$‐form (quadratic or bilinear) is defined over F$F$ for a field extension K/F$K/F$. We study this problem in a complete manner for K$K$‐quadratic and bilinear forms up to dimension 4 when F$F$ is a field of characteristic 2 and K$K$ is the function field of a projective quadric.

Date: 2025
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https://doi.org/10.1002/mana.202400061

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