Mathematics > Algebraic Geometry
[Submitted on 16 Dec 2018 (v1), last revised 29 Mar 2019 (this version, v3)]
Title:Künneth formulas for motives and additivity of traces
View PDFAbstract:We prove several Künneth formulas in motivic homotopy categories and deduce a Verdier pairing in these categories following SGA5, which leads to the characteristic class of a constructible motive, an invariant closely related to the Euler-Poincaré characteristic. We prove an additivity property of the Verdier pairing using the language of derivators, following the approach of May and Groth-Ponto-Shulman; using such a result we show that in the presence of a Chow weight structure, the characteristic class for all constructible motives is uniquely characterized by proper covariance, additivity along distinguished triangles, refined Gysin morphisms and Euler classes. In the relative setting, we prove the relative Künneth formulas under some transversality conditions, and define the relative characteristic class.
Submission history
From: Enlin Yang [view email][v1] Sun, 16 Dec 2018 10:44:04 UTC (46 KB)
[v2] Thu, 28 Mar 2019 14:41:55 UTC (64 KB)
[v3] Fri, 29 Mar 2019 12:30:04 UTC (64 KB)
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