Vol. 8, No. 8, 2014

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Relative cohomology of cuspidal forms on PEL-type Shimura varieties

Kai-Wen Lan and Benoît Stroh

Vol. 8 (2014), No. 8, 1787–1799

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.

Shimura varieties, vanishing theorem, toroidal compactification, minimal compactification, cuspidal forms
Mathematical Subject Classification 2010
Primary: 14G35
Secondary: 14K10, 14G17, 32L20
Received: 23 August 2013
Revised: 3 August 2014
Accepted: 8 October 2014
Published: 28 November 2014
Kai-Wen Lan
School of Mathematics
University of Minnesota
127 Vincent Hall
206 Church Street SE
Minneapolis, MN 55455
United States
Benoît Stroh
Université Paris 13
99 avenue J.B. Clément
93430 Villetaneuse