Koszul duality and extensions of exponential functors. (English) Zbl 1148.18008

The aim of this interesting paper is to study Koszul duals of some important functors and to apply the results to compute Ext-groups between exponential functors. One of the main results is Theorem 3.2. In this theorem the author computes the cohomology of the Koszul dual for the twisted divided power functor. Using this result, in the last section of the paper, explicit formulas for some Ext-groups are given (Corollaries 4.3, 4.4 and 4.5).


18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)
16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
18E30 Derived categories, triangulated categories (MSC2010)
18G40 Spectral sequences, hypercohomology
20G10 Cohomology theory for linear algebraic groups
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