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Analytic continuation on Shimura varieties with $μ$-ordinary locus

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Title: Analytic continuation on Shimura varieties with $μ$-ordinary locus
Authors: Bijakowski, S
Item Type: Report
Abstract: We study the geometry of unitary Shimura varieties without assuming the existence of an ordinary locus. We prove, by a simple argument, the existence of canonical subgroups on a strict neighborhood of the $mu$-ordinary locus (with an explicit bound). We then define the overconvergent modular forms (of classical weight), as well as the relevant Hecke operators. Finally, we show how an analytic continuation argument can be adapted to this case to prove a classicality theorem, namely that an overconvergent modular form which is an eigenform for the Hecke operators is classical under certain assumptions.
Issue Date: 13-May-2016
URI: http://hdl.handle.net/10044/1/26690
DOI: https://doi.org/10.25561/26690
Copyright Statement: © 2015 The Author
Keywords: math.NT
Notes: 36 pages
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences
Mathematics