[Complexes bar et extensions de foncteurs exponentiels classiques]
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.
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.
Keywords: Strict polynomial functors, extensions, bar complexes, Eilenberg-Mac Lane spaces, Frobenius twist
Mot clés : foncteurs strictement polynomiaux, extensions, complexes bar, espaces d’Eilenberg-Mac Lane, torsion de Frobenius
@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},
pages = {2563--2637},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {64},
number = {6},
year = {2014},
doi = {10.5802/aif.2921},
zbl = {06387348},
mrnumber = {3331175},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.2921/}
}
TY - JOUR AU - Touzé, Antoine TI - Bar complexes and extensions of classical exponential functors JO - Annales de l'Institut Fourier PY - 2014 SP - 2563 EP - 2637 VL - 64 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2921/ DO - 10.5802/aif.2921 LA - en ID - AIF_2014__64_6_2563_0 ER -
%0 Journal Article %A Touzé, Antoine %T Bar complexes and extensions of classical exponential functors %J Annales de l'Institut Fourier %D 2014 %P 2563-2637 %V 64 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2921/ %R 10.5802/aif.2921 %G en %F AIF_2014__64_6_2563_0
Touzé, Antoine. Bar complexes and extensions of classical exponential functors. Annales de l'Institut Fourier, Tome 64 (2014) no. 6, pp. 2563-2637. doi : 10.5802/aif.2921. http://www.numdam.org/articles/10.5802/aif.2921/
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