Koszul, Ringel, and Serre duality for strict polynomial functors

Abstract

This is a report on recent work of Chalupnik and Touze. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we connect this to Ringel duality for Schur algebras and describe Serre duality for strict polynomial functors.

23 pages. Version 2: Added correct assumptions for Serre duality and included further references. Version 3: Added dedication and made minor simplifications and corrections. Version 4: Final version (slightly updated) accepted for publication in Compositio Mathematica

References in corpus (1)

• Ringel duality and derivatives of non-additive functors

Cited by in corpus (10)

• Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology
• Exterior power operations on higher $K$-groups via binary complexes
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• Homological finiteness of functors on an additive category and applications
• Connectedness of cup products for polynomial representations of $G{L}_n$ and applications
• A construction of the universal classes for algebraic groups with the twisting spectral sequence
• Schur Algebras for the Alternating Group and Koszul Duality
• Ext-groups in the Category of Strict Polynomial Functors