Geodesic
The unramified two-dimensional Langlands correspondence
Izvestiya. Mathematics , Tome 77 (2013) no. 4, pp. 714-741

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe the unramified Langlands correspondence for two-dimensional local fields and construct a categorical analogue of the unramified principal series representation and study its properties. The main tool for this description is the construction of a certain central extension. For this and other central extensions, we prove non-commutative reciprocity laws (that is, splitting of the central extensions over certain subgroups) for arithmetic surfaces and projective surfaces over finite fields. These reciprocity laws connect central extensions constructed locally and globally.
Keywords: 2-vector spaces, two-dimensional local fields, higher adèles, generalized Langlands programme, two-dimensional non-commutative reciprocity laws. 
@article{IM2_2013_77_4_a5,
     author = {D. V. Osipov},
     title = {The unramified two-dimensional {Langlands} correspondence},
     journal = {Izvestiya. Mathematics },
     pages = {714--741},
     publisher = {mathdoc},
     volume = {77},
     number = {4},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a5/}
}
TY  - JOUR
AU  - D. V. Osipov
TI  - The unramified two-dimensional Langlands correspondence
JO  - Izvestiya. Mathematics 
PY  - 2013
SP  - 714
EP  - 741
VL  - 77
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a5/
LA  - en
ID  - IM2_2013_77_4_a5
ER  - 
%0 Journal Article
%A D. V. Osipov
%T The unramified two-dimensional Langlands correspondence
%J Izvestiya. Mathematics 
%D 2013
%P 714-741
%V 77
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a5/
%G en
%F IM2_2013_77_4_a5
D. V. Osipov. The unramified two-dimensional Langlands correspondence. Izvestiya. Mathematics , Tome 77 (2013) no. 4, pp. 714-741. http://geodesic.mathdoc.fr/item/IM2_2013_77_4_a5/