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Taylor towers for Γ -modules

Birgit Richter (2001)

Annales de l’institut Fourier

We consider Taylor approximation for functors from the small category of finite pointed sets Γ to modules and give an explicit description for the homology of the layers of the Taylor tower. These layers are shown to be fibrant objects in a suitable closed model category structure. Explicit calculations are presented in characteristic zero including an application to higher order Hochschild homology. A spectral sequence for the homology of the homotopy fibres of this approximation is provided.

The structure of the tensor product of 𝔽 2 [ - ] with a finite functor between 𝔽 2 -vector spaces

Geoffrey M. L. Powell (2000)

Annales de l'institut Fourier

The paper studies the structure of functors I F in the category of functors from finite dimensional 𝔽 2 -vector spaces to 𝔽 2 -vector spaces, where F is a finite functor and I is the injective functor V 𝔽 2 V * . A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors I F are artinian of type one.

Troesch complexes and extensions of strict polynomial functors

Antoine Touzé (2012)

Annales scientifiques de l'École Normale Supérieure

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 Ext -computations as well as new results. In particular, we get a cohomological version of the “fundamental theorems” from classical invariant theory for  G L n for  n big enough (and we give a conjecture for smaller values of  n ). We also study the “twisting spectral sequence” E s , t ( F , G , r ) converging to the extension groups Ext 𝒫 𝕜 * ( F ( r ) , G ( r ) ) between the...

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