2023/09/01 by Cassady, Connor
#11E04 #11E81 #13J10 #14G12 (primary) #14H25 #16W60 (secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2309.00689
We study anisotropic universal quadratic forms over semi-global fields; i.e., over one-variable function fields over complete discretely valued fields. In particular, given a semi-global field F, we compute both the m-invariant of F and the set of dimensions of anisotropic universal quadratic forms over F. We also define the strong m-invariant of a field k and show that it behaves analogously to the strong u-invariant of k, defined by Harbater, Hartmann, and Krashen. Our main tool in this study is the local-global principle for isotropy of quadratic forms over a semi-global field with respect to particular sets of overfields.