Geodesic
The category of singularities as a crystal and global Springer fibers
Arinkin, D.1 ; Gaitsgory, D.2
1 Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
2 Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Journal of the American Mathematical Society, Tome 31 (2018) no. 1, pp. 135-214

Voir la notice de l'article provenant de la source American Mathematical Society

We prove the “gluing conjecture” on the spectral side of the categorical geometric Langlands conjecture. The key tool is the structure of crystal on the category of singularities, which allows one to reduce the conjecture to the question of homological triviality of certain homotopy types. These homotopy types are obtained by gluing from a global version of Springer fibers.
DOI : 10.1090/jams/882

Arinkin, D. 1 ; Gaitsgory, D. 2

1 Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
2 Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138 
@article{10_1090_jams_882,
     author = {Arinkin, D. and Gaitsgory, D.},
     title = {The category of singularities as a crystal and global {Springer} fibers},
     journal = {Journal of the American Mathematical Society},
     pages = {135--214},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2018},
     doi = {10.1090/jams/882},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/jams/882/}
}
TY  - JOUR
AU  - Arinkin, D.
AU  - Gaitsgory, D.
TI  - The category of singularities as a crystal and global Springer fibers
JO  - Journal of the American Mathematical Society
PY  - 2018
SP  - 135
EP  - 214
VL  - 31
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/jams/882/
DO  - 10.1090/jams/882
ID  - 10_1090_jams_882
ER  - 
%0 Journal Article
%A Arinkin, D.
%A Gaitsgory, D.
%T The category of singularities as a crystal and global Springer fibers
%J Journal of the American Mathematical Society
%D 2018
%P 135-214
%V 31
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/jams/882/
%R 10.1090/jams/882
%F 10_1090_jams_882
Arinkin, D.; Gaitsgory, D. The category of singularities as a crystal and global Springer fibers. Journal of the American Mathematical Society, Tome 31 (2018) no. 1, pp. 135-214. doi: 10.1090/jams/882

[1] Arinkin, D., Gaitsgory, D. Singular support of coherent sheaves and the geometric Langlands conjecture Selecta Math. (N.S.) 2015 1 199

[2] Benson, Dave, Iyengar, Srikanth B., Krause, Henning Local cohomology and support for triangulated categories Ann. Sci. Éc. Norm. Supér. (4) 2008 573 619

[3] Drinfeld, V., Gaitsgory, D. Compact generation of the category of D-modules on the stack of 𝐺-bundles on a curve Camb. J. Math. 2015 19 125

[4] Gaitsgory, Dennis ind-coherent sheaves Mosc. Math. J. 2013

[5] Gaitsgory, Dennis Sheaves of categories and the notion of 1-affineness 2015 127 225

[6] Gaitsgory, Dennis Outline of the proof of the geometric Langlands conjecture for 𝐺𝐿₂ Astérisque 2015 1 112

[7] Gaitsgory, Dennis, Rozenblyum, Nick Crystals and D-modules Pure Appl. Math. Q. 2014 57 154

[8] Stevenson, Greg Subcategories of singularity categories via tensor actions Compos. Math. 2014 229 272

Cité par Sources :