Relative cohomology of cuspidal forms on Pel-Type shimura varieties

Kai Wen Lan, Benoît Stroh

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We present a short proof that, for PEL-type Shimura varieties, subcanonical extensions of automorphic bundles, whose global sections over toroidal compactifications of Shimura varieties are represented by cuspidal automorphic forms, have no higher direct images under the canonical morphism to the minimal compactification, in characteristic zero or in positive characteristics greater than an explicitly computable bound.

Original languageEnglish (US)
Pages (from-to)1787-1799
Number of pages13
JournalAlgebra and Number Theory
Issue number8
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© 2014 Mathematical Sciences Publishers.


  • Cuspidal forms
  • Minimal compactification
  • Shimura varieties
  • Toroidal compactification
  • Vanishing theorem


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