L-PACKETS AND A GEOMETRIC CONJECTURE FOR SL2(K) WITH K A LOCAL FUNCTION FIELD OF CHARACTERISTIC 2 - Mendes, S. (p-adics.2019 Seventh International Conference on p-Adic Mathematical Physics and its Applications, 2019)
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