Math @ Duke

Publications [#320416] of Jayce R. Getz
Papers Published
 Getz, JR; Getz, JR; Wambach, E, twisted relative trace formulae with a view towards unitary groupsTwisted relative trace formulae with a view towards unitary groups,
American Journal of Mathematics
(2012), Johns Hopkins University Press: American Journal of Mathematics
(last updated on 2017/12/14)
Abstract: We introduce a twisted relative trace formula which simultaneously generalizes
the twisted trace formula of Langlands et. al. (in the quadratic case) and the relative trace
formula of Jacquet and Lai [JL]. Certain matching statements relating this twisted relative
trace formula to a relative trace formula are also proven (including the relevant fundamental
lemma in the "biquadratic case"). Using recent work of Jacquet, Lapid and their collaborators
[J1] and the RankinSelberg integral representation of the Asai Lfunction (obtained by
Flicker using the theory of Jacquet, PiatetskiiShapiro, and Shalika [Fl2]), we give the following
application: Let E/F be a totally real quadratic extension, let
U '
be a quasisplit unitary group with respect to a CM extension M/F, and let U := U'_E .
Under suitable local hypotheses, we show that a cuspidal cohomological automorphic representation
of U whose Asai Lfunction has a pole at the edge of the critical strip is
nearly equivalent to a cuspidal cohomological automorphic representation 0 of U that is
U 'distinguished in the sense that there is a form in the space of 0 admitting a nonzero
period over U . This provides cohomologically nontrivial cycles of middle dimension on unitary
Shimura varieties analogous to those on Hilbert modular surfaces studied by Harder,
Langlands, and Rapoport [HLR].


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