A note on quadratic forms

2023/08/03 by Fabian Hebestreit, Achim Krause, Hebestreit, Fabian +3
Mathematics · #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2308.01795

Abstract

For a field extension L/K we consider maps that are quadratic over L but whose polarisation is only bilinear over K. Our main result is that all such are automatically quadratic forms over L in the usual sense if and only if L/K is formally unramified. In particular, this shows that over finite and number fields, one of the axioms in the standard definition of quadratic forms is superfluous.

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