On quadratic distinction of automorphic sheaves

Yifeng Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We prove a geometric version of a classical result on the characterization of an irreducible cuspidal automorphic representation of being the base change of a stable cuspidal representation of the quasi-split unitary group associated to the quadratic extension E/F, via the nonvanishing of certain period integrals, called being distinguished. We show that certain cohomology of an automorphic sheaf of GL n,X is nonvanishing if and only if the corresponding local system E on X is conjugate self-dual with respect to an étale double cover X′/X of curves, which directly relates to the base change from the associated unitary group. In particular, the geometric setting makes sense over any base field.

Original languageEnglish (US)
Pages (from-to)5328-5360
Number of pages33
JournalInternational Mathematics Research Notices
Issue number23
StatePublished - Dec 2012

ASJC Scopus subject areas

  • Mathematics(all)


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