On spectra and affine strict polynomial functors
[Sur les spectres et les foncteurs affines strictement polynomiaux]
Chałupnik, Marcin1
1 Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02–097 Warsaw (Poland)
Annales de l'Institut Fourier, Online first, 30 p.

Nous comparons des catégories dérivés de la catégorie des foncteurs strictement polynomiaux sur un domaine et la catégorie des endofoncteurs ordinaires sur la catégorie des espaces vectoriels. Nous introduisons deux catégories intermédiaires : la catégorie de foncteurs ∞-affines strictement polynomiaux et la catégorie des spectres des foncteurs strictement polynomiaux. Ils fournissent un cadre conceptuel pour les théorèmes de calcul de Franjou–Friedlander–Scorichenko–Suslin et clarifient le rôle de l’inversion du morphisme de Frobenius dans la comparaison entre cohomologie rationnelle et discrète.

We compare derived categories of the category of strict polynomial functors over a finite field and the category of ordinary endofunctors on the category of vector spaces. We introduce two intermediate categories: the category of ∞-affine strict polynomial functors and the category of spectra of strict polynomial functors. They provide a conceptual framework for computational theorems of Franjou–Friedlander–Scorichenko–Suslin and clarify the role of inverting the Frobenius morphism in the comparison between rational and discrete cohomology.

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DOI : 10.5802/aif.3666
Classification : 18A25, 18A40, 18G15
Keywords: Strict polynomial functor, Affine functor, Spectrum, Ext-group.
Mot clés : Foncteur strictement polynomial, foncteur affine, spectre, Ext-groupe.
Chałupnik, Marcin 1

1 Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02–097 Warsaw (Poland) 
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Chałupnik, Marcin. On spectra and affine strict polynomial functors. Annales de l'Institut Fourier, Online first, 30 p.

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