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

Jesse Pajwani; Ambrus Pál

doi:10.2140/akt.2025.10.123

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

Jesse Pajwani, Ambrus Pál

Department of Mathematical Sciences

Imperial College London

Research output: Contribution to journal › Article › peer-review

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 our power structure is compatible with the variety power structure when we restrict to varieties of dimension 0, using techniques of Garibaldi, Merkurjev and Serre about cohomological invariants.

Original language	English
Pages (from-to)	123-152
Number of pages	30
Journal	Annals of K-Theory
Volume	10
Issue number	2
DOIs	https://doi.org/10.2140/akt.2025.10.123
Publication status	Published - 19 Mar 2025

Keywords

Euler characteristic
motivic homotopy
power structures
symmetric powers

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.2140/akt.2025.10.123

https://arxiv.org/abs/2309.03366

Cite this

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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