Algebra & Number Theory

Relative cohomology of cuspidal forms on PEL-type Shimura varieties

Kai-Wen Lan and 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.

Article information

Algebra Number Theory, Volume 8, Number 8 (2014), 1787-1799.

Received: 23 August 2013
Revised: 3 August 2014
Accepted: 8 October 2014
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
Secondary: 14K10: Algebraic moduli, classification [See also 11G15] 14G17: Positive characteristic ground fields 32L20: Vanishing theorems

Shimura varieties vanishing theorem toroidal compactification minimal compactification cuspidal forms


Lan, Kai-Wen; Stroh, Benoît. Relative cohomology of cuspidal forms on PEL-type Shimura varieties. Algebra Number Theory 8 (2014), no. 8, 1787--1799. doi:10.2140/ant.2014.8.1787.

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