Hyperbolicity over function fields of quadrics

2017/08/05 by O'Shea, James
#11E04 #11E16 #11E81 #12F20 #14E05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.01782

Abstract

A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolicity over function fields, and to recover a number of important established results in quadratic form theory by means of novel, short and elementary proofs.

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