Motivic equivalence of affine quadrics
Tom Bachmann, Alexander Vishik
TL;DR
This paper demonstrates that the motive of an affine quadric uniquely determines the associated quadratic form, establishing a link between geometric motives and algebraic quadratic forms.
Contribution
It proves that the motive of an affine quadric completely determines the quadratic form, a novel result connecting motives and quadratic form classification.
Findings
The motive of an affine quadric determines the quadratic form.
Affine quadrics' motives encode complete information about the quadratic form.
This result bridges algebraic geometry and quadratic form theory.
Abstract
In this article we show that the motive of an affine quadric {q = 1} determines the respective quadratic form.
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