Parametrizing Shimura subvarieties of A1A1 Shimura varieties and related geometric problems

Title:
Parametrizing Shimura subvarieties of A1A1 Shimura varieties and related geometric problems
Authors:
Linowitz, Benjamin; Stover, Matthew
Abstract:
This paper gives a complete parametrization of the commensurability classes of totally geodesic subspaces of irreducible arithmetic quotients of Xa,b=(H2)a×(H3)bXa,b=(H2)a×(H3)b . A special case describes all Shimura subvarieties of type A1A1 Shimura varieties. We produce, for any n≥1n≥1 , examples of manifolds/Shimura varieties with precisely n commensurability classes of totally geodesic submanifolds/Shimura subvarieties. This is in stark contrast with the previously studied cases of arithmetic hyperbolic 3-manifolds and quaternionic Shimura surfaces, where the presence of one commensurability class of geodesic submanifolds implies the existence of infinitely many classes.
Citation:
Linowitz, Benjamin, and Matthew Stover. 2016. “Parameterizing Shimura subvarieties of A1 Shimura varieties and related geometric problems.” Archiv der Mathematik 107(3): 213-226.
Publisher:
Springer Verlag
DATE ISSUED:
2016-09
Department:
Mathematics
Type:
Article
PUBLISHED VERSION:
10.1007/s00013-016-0944-9
PERMANENT LINK:
http://hdl.handle.net/11282/620428

Full metadata record

DC FieldValue Language
dc.contributor.authorLinowitz, Benjaminen
dc.contributor.authorStover, Matthewen
dc.date.accessioned2017-05-12T14:04:22Z-
dc.date.available2017-05-12T14:04:22Z-
dc.date.issued2016-09-
dc.identifier.citationLinowitz, Benjamin, and Matthew Stover. 2016. “Parameterizing Shimura subvarieties of A1 Shimura varieties and related geometric problems.” Archiv der Mathematik 107(3): 213-226.en
dc.identifier.issn0003-889X-
dc.identifier.urihttp://hdl.handle.net/11282/620428-
dc.description.abstractThis paper gives a complete parametrization of the commensurability classes of totally geodesic subspaces of irreducible arithmetic quotients of Xa,b=(H2)a×(H3)bXa,b=(H2)a×(H3)b . A special case describes all Shimura subvarieties of type A1A1 Shimura varieties. We produce, for any n≥1n≥1 , examples of manifolds/Shimura varieties with precisely n commensurability classes of totally geodesic submanifolds/Shimura subvarieties. This is in stark contrast with the previously studied cases of arithmetic hyperbolic 3-manifolds and quaternionic Shimura surfaces, where the presence of one commensurability class of geodesic submanifolds implies the existence of infinitely many classes.en
dc.language.isoen_USen
dc.publisherSpringer Verlagen
dc.identifier.doi10.1007/s00013-016-0944-9-
dc.subject.departmentMathematicsen_US
dc.titleParametrizing Shimura subvarieties of A1A1 Shimura varieties and related geometric problemsen_US
dc.typeArticleen
dc.identifier.journalArchiv der Mathematiken
dc.identifier.volume107en_US
dc.identifier.issue3en_US
dc.identifier.startpage213en_US
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