Dans cette note on donne une esquisse de la démonstration d’une conjecture de [13] qui établit un lien entre le faisceau correspondant à la série d’Eisenstein géométrique et la cohomologie semi-infinie du petit groupe quantique à coefficients dans le module basculant pour le groupe quantique de Lusztig.
We sketch a proof of a conjecture of [13] that relates the geometric Eisenstein series sheaf with semi-infinite cohomology of the small quantum group with coefficients in the tilting module for the big quantum group.
@article{AFST_2016_6_25_2-3_235_0,
author = {D. Gaitsgory},
title = {Eisenstein series and quantum groups},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {235--315},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 25},
number = {2-3},
year = {2016},
doi = {10.5802/afst.1495},
zbl = {1411.14020},
mrnumber = {3530159},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1495/}
}
TY - JOUR AU - D. Gaitsgory TI - Eisenstein series and quantum groups JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2016 SP - 235 EP - 315 VL - 25 IS - 2-3 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1495/ DO - 10.5802/afst.1495 LA - en ID - AFST_2016_6_25_2-3_235_0 ER -
%0 Journal Article %A D. Gaitsgory %T Eisenstein series and quantum groups %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2016 %P 235-315 %V 25 %N 2-3 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1495/ %R 10.5802/afst.1495 %G en %F AFST_2016_6_25_2-3_235_0
D. Gaitsgory. Eisenstein series and quantum groups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, parties 1 et 2, Tome 25 (2016) no. 2-3, pp. 235-315. doi : 10.5802/afst.1495. https://afst.centre-mersenne.org/articles/10.5802/afst.1495/
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