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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Local base change via Tate cohomology
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by Niccolò Ronchetti
Represent. Theory 20 (2016), 263-294
Published electronically: September 27, 2016


We propose a new way to realize cyclic base change (a special case of Langlands functoriality) for prime degree extensions of characteristic zero local fields. Let $F / E$ be a prime degree $l$ extension of local fields of residue characteristic $p \neq l$. Let $\pi$ be an irreducible cuspidal $l$-adic representation of $\mathrm {GL}_n(E)$ and let $\rho$ be an irreducible cuspidal $l$-adic representation of $\mathrm {GL}_n(F)$ which is Galois-invariant. Under some minor technical conditions on $\pi$ and $\rho$ (for instance, we assume that both are level zero) we prove that the $\bmod l$-reductions $r_l(\pi )$ and $r_l(\rho )$ are in base change if and only if the Tate cohomology of $\rho$ with respect to the Galois action is isomorphic, as a modular representation of $\mathrm {GL}_n(E)$, to the Frobenius twist of $r_l(\pi )$. This proves a special case of a conjecture of Treumann and Venkatesh as they investigate the relationship between linkage and Langlands functoriality.
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Bibliographic Information
  • Niccolò Ronchetti
  • Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
  • Email:
  • Received by editor(s): July 2, 2015
  • Received by editor(s) in revised form: April 21, 2016, and July 18, 2016
  • Published electronically: September 27, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Represent. Theory 20 (2016), 263-294
  • MSC (2010): Primary 11F70, 11S37, 22E50
  • DOI:
  • MathSciNet review: 3551160