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We develop a new approach of extension calculus in the category of strict polynomial functors, based on Troesch complexes. We obtain new short elementary proofs of numerous classical -computations as well as new results.
In particular, we get a cohomological version of the “fundamental theorems” from classical invariant theory for for big enough (and we give a conjecture for smaller values of ).
We also study the “twisting spectral sequence” converging to the extension groups between the...
We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and bridges these Ext-groups with the homology of Eilenberg-Mac Lane spaces.
This article completes earlier results of the author, and provides an alternative approach to classical Ext-computations in the category of strict polynomial functors over fields....
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