On Serre functor in the category of strict polynomial functors

2016/03/19 by Marcin Chałupnik, Chałupnik, Marcin
Mathematics · #18A25 #18A40 #18G15 #20G15 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:18A25 #msc:18A40 #msc:18G15 #msc:20G15

paper · pdf · doi:10.48550/arxiv.1603.06128

arxiv created 2016/03/19 · openalex publication_date 2016/03/19 · arxiv updated 2016/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study a Serre functor in the category \cal P_d of strict polynomial functors over a field of positive characteristic. By using it we obtain the Poincaré duality formula for Ext--groups from [C3] in elementary way. We also show that the derived category of the category of affine strct polynomial functors in some cases carries the structure of Calabi-Yau category.

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