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Power structures on the Grothendieck--Witt ring and the motivic Euler characteristic

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arxiv 2309.03366 v3 pith:SI6IQEDE submitted 2023-09-06 math.NT

Jesse Pajwani , Ambrus Pál This is my paper · ORCID
classification math.NT
keywords powerstructurecharacteristiccompatibleeulergrothendieck--wittmotivicring
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abstract

For $k$ a field, we construct a power structure on the Grothendieck--Witt ring of $k$ which has the potential to be compatible with symmetric powers of varieties and the motivic Euler characteristic. We then show this power structure is compatible with the power structure when we restrict to varieties of dimension $0$.

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  1. Quadratically Enriched Plane Curve Counting via Tropical Geometry

    math.AG 2025-02 conditional novelty 7.0 of 10

    A correspondence theorem equates quadratically enriched algebraic curve counts with conjugate point conditions to tropical counts with double point conditions, and a floor diagram algorithm computes them.

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