A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula
By Marc Hoyois. 2013
126 citations recorded by the source corpus.
We prove a trace formula in stable motivic homotopy theory over a general base scheme, equating the trace of an endomorphism of a smooth proper scheme with the "Euler characteristic integral" of a certain cohomotopy class over its scheme of fixed points. When the base is a field and the fixed points are \'etale, we compute this integral in terms of Morel's identification of the ring of endomorphisms of the motivic sphere spectrum with the Grothendieck-Witt ring. In particular, we show that the Euler characteristic of an \'etale algebra corresponds to the class of its trace form in the Grothendieck-Witt ring.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/60b0844cbe875311cebee460c7040d9c14efbbbd
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In Geometry and Topology
- M. Levine
- Markus Spitzweck
- O. Rondigs
- Vladimir Voevodsky
- Thomas H. Geisser
- P. Ostvaer
- Frédéric Déglise
- P. Østvær
In Mathematical Physics
- M. Levine
- Markus Spitzweck
- O. Rondigs
- P. Ostvaer
- Thomas H. Geisser
- Frédéric Déglise
- P. Østvær
- Ivan Panin
Citations in the corpus
- Aspects of Enumerative Geometry with Quadratic Forms (2017, methodology): “The foundations of this theory have been laid by work of Barge-Morel [7], Fasel [14], Fasel-Srinivas [15] and Morel [34, 35] (and many others), and first steps in this direction have been taken by Hoyois [20], Kass-Wickelgren [24, 25] and Pauli [42].”