Mathematical Research Letters

Volume 25 (2018)

Number 1

Dual BGG complexes for automorphic bundles

Pages: 85 – 141



Kai-Wen Lan (School of Mathematics, University of Minnesota, Minneapolis, Mn., U.S.A.)

Patrick Polo (Institut de Mathématiques, Université Pierre et Marie Curie, Paris, France)


We generalize the construction of dual BGG complexes in Faltings–Chai and Mokrane–Tilouine–Polo (from the case of Siegel modular varieties) to all smooth integral models of PEL-type Shimura varieties.


Shimura varieties, automorphic bundles and differential operators, BGG and dual BGG complexes

2010 Mathematics Subject Classification

Primary 11G18. Secondary 11F55, 11G15, 17B50, 20G30.

The research of the first author is partially supported by the Qiu Shi Science and Technology Foundation, by the National Science Foundation under agreements Nos. DMS-0635607, DMS-1069154, DMS-1258962, and DMS-1352216, and by an Alfred P. Sloan Research Fellowship.

Received 16 February 2016

Accepted 18 July 2016

Published 4 June 2018