Satake compactification of analytic Drinfeld modular varieties

JOURNAL OF NUMBER THEORY

卷:219

Article

Haberli, Simon¹ 

[1] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

关键词: Function field arithmetic;    Drinfeld modules;    Drinfeld moduli schemes;    Drinfeld upper half space;    Drinfeld modular forms;    Compactification;    Rigid analytic geometry;   

DOI  :  10.1016/j.jnt.2020.09.018

来源: Elsevier

【 摘 要 】

We construct a normal projective rigid analytic compactification of an arbitrary Drinfeld modular variety whose boundary is stratified by modular varieties of smaller dimensions. This generalizes work of Kapranov. Using an algebraic modular compactification that generalizes Pink and Schieder's, we show that the analytic compactification is naturally isomorphic to the analytification of Pink's normal algebraic compactification. We interpret analytic Drinfeld modular forms as the global sections of natural ample invertible sheaves on the analytic compactification and deduce finiteness results for spaces of such modular forms. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free