Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-11T00:13:30.271Z Has data issue: false hasContentIssue false

$L$-INDISTINGUISHABILITY ON EIGENVARIETIES

Published online by Cambridge University Press:  22 March 2016

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

Abstract

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

Type
Research Article
Copyright
© Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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), 205310. 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), 582634.CrossRefGoogle Scholar
Buzzard, K., Eigenvarieties, in L-Functions and Galois Representations, London Mathematical Society Lecture Note Series, Volume 320, pp. 59120 (Cambridge University Press, Cambridge, 2007).CrossRefGoogle Scholar
Chenevier, G., Familles p-adiques de formes automorphes pour GL n , J. Reine Angew. Math. 570 (2004), 143217.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), 726785.CrossRefGoogle Scholar
Loeffler, D., Overconvergent algebraic automorphic forms, Proc. Lond. Math. Soc. (3) 102(2) (2011), 193228.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), 45111.CrossRefGoogle Scholar