Mathematical Research Letters

Volume 29 (2022)

Number 2

Closed immersions of toroidal compactifications of Shimura varieties

Pages: 487 – 528



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


We explain that any closed immersion between Shimura varieties defined by morphisms of Shimura data extends to some closed immersion between their projective smooth toroidal compactifications, up to refining the choices of cone decompositions. We also explain that the same holds for many closed immersions between integral models of Shimura varieties and their toroidal compactifications available in the literature.

The author was partially supported by the National Science Foundation under agreement No. DMS-1352216, and by a Simons Fellowship in Mathematics.

Received 4 January 2020

Accepted 30 November 2020

Published 29 September 2022