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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...

Unstable homotopy invariance for finite fields

Kevin P. Knudson (2002)

Fundamenta Mathematicae

We prove that if k is a finite field with p d elements, then the natural map H i ( G L ( k ) , ) H i ( G L ( k [ t ] ) , ) is an isomorphism for 0 ≤ i < d(p-1) and for all n.

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