Abstract 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.

中文翻译：

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解析 Drinfeld 模变体的 Satake 紧致化

摘要 我们构造了一个任意 Drinfeld 模变体的正规射影刚性解析紧化，其边界由较小维度的模变体分层。这概括了 Kapranov 的工作。使用推广 Pink 和 Schieder 的代数模紧化，我们表明解析紧化与 Pink 的正常代数紧化的解析自然同构。我们将解析 Drinfeld 模形式解释为解析紧化上的自然充足可逆滑轮的全局部分，并推导出此类模形式空间的有限性结果。