 
Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & SpringerVerlag
Zbl 1122.11034
Rajan, C.S.
On Langlands functoriality reduction to the semistable case. (English)
Dani, S. G. (ed.) et al., Algebraic groups and arithmetic. Proceedings of the interna
tional conference, Mumbai, India, December 1722, 2001. New Delhi: Narosa Publish
ing House/Published for the Tata Institute of Fundamental Research. 199219 (2004).
ISBN 8173196184/hbk
Langlands' philosophy predicts that an Lmorphism between the Lgroups of two con
nected reductive groups gives rise to a transfer of automorphic forms of one group to
the other. The paper is meant to enunciate a principle according to which the trans
fer corresponding to an Lmorphism can be defined for all the members of a class of
automorphic representations if it can be defined for a suitably defined "nice" subclass
of representations, provided the class satisfies some properties like closure under tak
ing cyclic base change. This principle has its origin in the work of D. Blasius and D.
Ramakrishnan [Publ., Math. Sci. Res. Inst. 16, 3377 (1989; Zbl 0699.10043)]. The
author proves the following theorem to illustrate the principle: Let F be a number field,
and let : GF GLn(Ql) be an irreducible adic representation of GF . Suppose
for any finite solvable extension K/F, such that the restriction K
