Analytic continuation on Shimura varieties with mu-ordinary locus

作者：Bijakowski Stephane^*

来源：Algebra and Number Theory, 2016, 10(4): 843-885.

DOI：10.2140/ant.2016.10.843

• Shimura variety
• overconvergent modular forms
• mu-ordinary locus
• canonical subgroups

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.

• 出版日期2016