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<p>We prove the existence of a sequence of commutative diagrams generalizing the results on cohomology at infinity described in Ash and McConnell (Duke Math J 90:549–576, 1997) to the context of the well-tempered complex introduced in McConnell and MacPherson (Computing Hecke operators for arithmetic subgroups of general linear groups, http://arxiv.org/abs/2010.06036, 2020). Our main theorem provides a method for computing in finite terms the action of Hecke operators on the cohomology of the Borel-Serre boundary for the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\text {SL} _n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>SL</mtext> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> symmetric space.</p>

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Cohomology at infinity and the well-tempered complex

  • 期刊论文

  • 发表日期：

    2025年10月18日

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  • Dylan Galt,
  • Mark McConnell

摘要

We prove the existence of a sequence of commutative diagrams generalizing the results on cohomology at infinity described in Ash and McConnell (Duke Math J 90:549–576, 1997) to the context of the well-tempered complex introduced in McConnell and MacPherson (Computing Hecke operators for arithmetic subgroups of general linear groups, http://arxiv.org/abs/2010.06036, 2020). Our main theorem provides a method for computing in finite terms the action of Hecke operators on the cohomology of the Borel-Serre boundary for the \(\text {SL} _n\) SL n symmetric space.