Soit un anneau polynomial à variables et soit une suite strictement croissante de nombres entiers. Boij et Söderberg ont conjecturé l’existence de -modules gradués de longueur finie ayant une résolution pure et libre de type dans le sens ou pour les générateurs du -ème module de syzygies de sont uniquement de degré .
Cet article présente une construction, en caractéristique zéro, de modules avec cette propriété qui sont aussi -équivariants. La construction fonctionne aussi pour les anneaux de la forme où est un anneau polynomial comme ci-dessus et est une algèbre extérieure.
Let be a polynomial ring in variables and let be a strictly increasing sequence of integers. Boij and Söderberg conjectured the existence of graded -modules of finite length having pure free resolution of type in the sense that for the -th syzygy module of has generators only in degree .
This paper provides a construction, in characteristic zero, of modules with this property that are also -equivariant. Moreover, the construction works over rings of the form where is a polynomial ring as above and is an exterior algebra.
Classification : 13D02, 13C14, 14M12, 20G05
Mots clés : résolution pure, résolution équivariante, diagramme de Betti, théorie de Boij-Söderberg
@article{AIF_2011__61_3_905_0, author = {Eisenbud, David and Fl\o ystad, Gunnar and Weyman, Jerzy}, title = {The existence of equivariant pure free resolutions}, journal = {Annales de l'Institut Fourier}, pages = {905--926}, publisher = {Association des Annales de l'institut Fourier}, volume = {61}, number = {3}, year = {2011}, doi = {10.5802/aif.2632}, mrnumber = {2918721}, zbl = {1239.13023}, language = {en}, url = {www.numdam.org/item/AIF_2011__61_3_905_0/} }
Eisenbud, David; Fløystad, Gunnar; Weyman, Jerzy. The existence of equivariant pure free resolutions. Annales de l'Institut Fourier, Tome 61 (2011) no. 3, pp. 905-926. doi : 10.5802/aif.2632. http://www.numdam.org/item/AIF_2011__61_3_905_0/
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