Resumen de Koszul duality and extensions of exponential functors

Marcin Chalupnik

• We study Koszul duality in the category of strict polynomial functors. We compute Koszul duals of various functors and apply these results to the problem of calculating Ext-groups between exponential functors. The main application is a full description of the Ext-groups between twisted exterior and divided powers and between twisted symmetric and divided powers which completes the program started in [V. Franjou, E. Friedlander, A. Scorichenko, A. Suslin, General linear and functor cohomology over finite fields, Ann. of Math. 150 (2) (1999) 663�728].