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Analytic continuation on Shimura varieties with $μ$-ordinary locus
File | Description | Size | Format | |
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1504.07423v1.pdf | Working paper | 370.48 kB | Adobe PDF | View/Open |
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 |