Geodesic
Categorical traces and a relative Lefschetz–Verdier formula
Forum of Mathematics, Sigma, Tome 10 (2022)

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We prove a relative Lefschetz–Verdier theorem for locally acyclic objects over a Noetherian base scheme. This is done by studying duals and traces in the symmetric monoidal $2$-category of cohomological correspondences. We show that local acyclicity is equivalent to dualisability and deduce that duality preserves local acyclicity. As another application of the category of cohomological correspondences, we show that the nearby cycle functor over a Henselian valuation ring preserves duals, generalising a theorem of Gabber. 
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     author = {Qing Lu and Weizhe Zheng},
     title = {Categorical traces and a relative {Lefschetz{\textendash}Verdier} formula},
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Qing Lu; Weizhe Zheng. Categorical traces and a relative Lefschetz–Verdier formula. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.2

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