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2 results

  • A twisted topological trace formula for Hecke operators and liftings from symplectic to general linear groups

  • Part of
  • Uwe Weselmann
  • Journal:
    Compositio Mathematica / Volume 148 / Issue 1 / January 2012
    Published online by Cambridge University Press:
    09 November 2011, pp. 65-120
    Print publication:
    January 2012
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  • For the locally symmetric space X attached to an arithmetic subgroup of an algebraic group G of ℚ-rank r, we construct a compact manifold by gluing together 2r copies of the Borel–Serre compactification of X. We apply the classical Lefschetz fixed point formula to and get formulas for the traces of Hecke operators ℋ acting on the cohomology of X. We allow twistings of ℋ by outer automorphisms η of G. We stabilize this topological trace formula and compare it with the corresponding formula for an endoscopic group of the pair (G,η) . As an application, we deduce a weak lifting theorem for the lifting of automorphic representations from Siegel modular groups to general linear groups.

  • Cycles on Arithmetic Surfaces

  • Ahmed Abbes
  • Journal:
    Compositio Mathematica / Volume 122 / Issue 1 / May 2000
    Published online by Cambridge University Press:
    04 December 2007, pp. 23-111
    Print publication:
    May 2000
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  • We develop a localized intersection theory for arithmetic schemes on the model of Fulton's intersection theory. We prove a Lefschetz fixed point formula for arithmetic surfaces, and give an application to a conjecture of Serre on the existence of Artin's representations for regular local rings of dimension 2 and unequal characteristic.