Vanishing theorems for coherent automorphic cohomologyReport as inadecuate

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Research in the Mathematical Sciences

, 3:39

First Online: 10 November 2016Received: 24 April 2015Accepted: 22 September 2016


We consider the coherent cohomology of toroidal compactifications of locally symmetric varieties such as Shimura varieties with coefficients in the canonical and subcanonical extensions of automorphic vector bundles, and give explicit conditions for them to vanish in certain degrees. We also provide algorithms for determining all such degrees in practice.

KeywordsLocally symmetric varieties Shimura varieties Toroidal compactifications Automorphic bundles Canonical extensions Vanishing theorems Coherent cohomology Mathematics Subject ClassificationPrimary 11G18 Secondary 14F17 14F30 11F75  Download fulltext PDF

Author: Kai-Wen Lan


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