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$L$-INDISTINGUISHABILITY ON EIGENVARIETIES

Part of: Arithmetic problems. Diophantine geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  22 March 2016

Judith Ludwig
Judith Ludwig*
Affiliation:
University of Bonn, Germany (jludwig@math.uni-bonn.de)
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Abstract

In this article, we construct examples of $L$-indistinguishable overconvergent eigenforms for an inner form of $\text{SL}_{2}$.

Keywords

p-adic Langlands programmeeigenvarietiesL-packets

MSC classification

Primary: 11F85: $p$-adic theory, local fields 11F12: Automorphic forms, one variable 14G22: Rigid analytic geometry
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 17 , Issue 2 , April 2018 , pp. 425 - 440
Copyright
© Cambridge University Press 2016 

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References

Bellaïche, J. and Chenevier, G., Families of Galois representations and Selmer groups, Astérisque 324 (2009), xii+314.Google Scholar
Breuil, C. and Mézard, A., Multiplicités modulaires et représentations de GL2(Z p ) et de Gal(Q p ̄/Q p ) en l = p , Duke Math. J. 115(2) (2002), 205–310. With an appendix by Guy Henniart.Google Scholar
Bushnell, C. J. and Kutzko, P. C., Smooth representations of reductive p-adic groups: structure theory via types, Proc. Lond. Math. Soc. (3) 77(3) (1998), 582–634.CrossRefGoogle Scholar
Buzzard, K., Eigenvarieties, in L-Functions and Galois Representations, London Mathematical Society Lecture Note Series, Volume 320, pp. 59–120 (Cambridge University Press, Cambridge, 2007).CrossRefGoogle Scholar
Chenevier, G., Familles p-adiques de formes automorphes pour GL n , J. Reine Angew. Math. 570 (2004), 143–217.Google Scholar
Gelbart, S. S., Automorphic Forms on Adèle Groups, Annals of Mathematics Studies, Volume 83 (Princeton University Press, Princeton, NJ, 1975). (University of Tokyo Press, Tokyo).CrossRefGoogle Scholar
Jacquet, H. and Langlands, R. P., Automorphic Forms on GL(2), Lecture Notes in Mathematics, Volume 114 (Springer-Verlag, Berlin–New York, 1970).CrossRefGoogle Scholar
Labesse, J.-P. and Langlands, R. P., L-indistinguishability for SL(2), Canad. J. Math. 31(4) (1979), 726–785.CrossRefGoogle Scholar
Loeffler, D., Overconvergent algebraic automorphic forms, Proc. Lond. Math. Soc. (3) 102(2) (2011), 193–228.CrossRefGoogle Scholar
Ludwig, J., A $p$ -adic Labesse–Langlands transfer, Preprint, 2014, arXiv:1412.4140.Google Scholar
Ramakrishnan, D., Modularity of the Rankin–Selberg L-series, and multiplicity one for SL(2), Ann. of Math. (2) 152(1) (2000), 45–111.CrossRefGoogle Scholar