On the Serre Functor in the Category of Strict Polynomial Functors

Abstract

We study a Serre functor in functor categories related to the category $\mathcal {P}_{d}$ P d of strict polynomial functors over a field of positive characteristic. Our main result shows that the derived category of the category of affine strict polynomial functors in some cases carries the structure of Calabi–Yau category. We also re-obtain the Poincaré duality formulas for Ext groups in $\mathcal {P}_{d}$ P d and construct a certain recollement diagram relating the derived categories of affine and ordinary strict polynomial functors.