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L-PACKETS AND A GEOMETRIC CONJECTURE FOR SL2(K) WITH K A LOCAL FUNCTION FIELD OF CHARACTERISTIC 2
Event Title
p-adics.2019 Seventh International Conference on p-Adic Mathematical Physics and its Applications
Year (definitive publication)
2019
Language
English
Country
Portugal
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Abstract
Abstract. Let G = SL2(K) with K a local function field of characteristic 2. In [3], the authors studied depth for G and its inner forms. Continuing the study of the group G from the point of view of local Langlands correspondence, we review Artin-Schreier theory for the field K, and show that this leads to a parametrization of certain L-packets in the smooth dual of G. We relate this with the geometric conjecture of Aubert-Baum-Plymen-Solleveld [1, 2] (see also [4] for the case of SL4 over a local field of characteristic zero). Joint work with Roger Plymen.
References:
[1] A-M. Aubert, P. Baum, R. J. Plymen, M. Solleveld, (2014). Geometric structure in
smooth dual and local Langlands conjecture. Japanese Journal of Mathematics, 9(2),
99{136. DOI: doi:10.1007/s11537-014-1267-x.
[2] A-M. Aubert, P. Baum, R. J. Plymen, M. Solleveld, (2017). Conjectures about padic groups and their noncommutative geometry. Contemporary Mathematics. DOI:
10.1090/conm/691/13892
[3] A-M. Aubert, S. Mendes, R.J. Plymen, M. Solleveld, (2017). On L-packets and depth
for SL2(K) and its inner form. International Journal of Number Theory, 1-19. DOI:
10.1142/S1793042117501421
[4] K. F. Chao, R. J. Plymen, (2012). Geometric structure in the tempered dual of SL(4).
Bulletin of the London Mathematical Society, 44, 1-9. DOI: 10.1112/blms/bdr106
Acknowledgements
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Keywords
local field,depth,Local langlands correspondence
Fields of Science and Technology Classification
- Mathematics - Natural Sciences
