Bar complexes and extensions of classical exponential functors
Annales de l'Institut Fourier, Volume 64 (2014) no. 6, p. 2563-2637

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. We also obtain significant Ext-computations for strict polynomial functors over the integers.

Nous calculons les groupes d’Ext entre foncteurs exponentiels classiques (i.e. puissances symétriques, extérieures ou divisées), et leur précomposition par le foncteur de torsion de Frobenius. Notre méthode repose sur les constructions bar, et relie ces calculs d’Ext avec l’homologie des espaces d’Eilenberg et Mac Lane.

Cet article complète des résultats précédents de l’auteur, et fournit une approche alternative aux calculs d’Ext classiques dans la catégorie des foncteurs strictement polynomiaux sur un corps. Nous obtenons aussi des calculs d’Ext notables pour les foncteurs strictement polynomiaux sur les entiers.

DOI : https://doi.org/10.5802/aif.2921
Classification:  18G15,  57T30,  20G10
Keywords: Strict polynomial functors, extensions, bar complexes, Eilenberg-Mac Lane spaces, Frobenius twist
@article{AIF_2014__64_6_2563_0,
     author = {Touz\'e, Antoine},
     title = {Bar complexes and extensions of classical exponential functors},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {64},
     number = {6},
     year = {2014},
     pages = {2563-2637},
     doi = {10.5802/aif.2921},
     mrnumber = {3331175},
     zbl = {06387348},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2014__64_6_2563_0}
}
Touzé, Antoine. Bar complexes and extensions of classical exponential functors. Annales de l'Institut Fourier, Volume 64 (2014) no. 6, pp. 2563-2637. doi : 10.5802/aif.2921. http://www.numdam.org/item/AIF_2014__64_6_2563_0/

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