广义自守层与Hirzebruch-Mumford比例原理
Generalized automorphic sheaves and the proportionality principle of Hirzebruch-Mumford
摘要：
我们公理化了（混合）Shimura簇及其自守向量丛的环面紧化的代数性质。本文提出了广义自守层的概念，它包含了自守向量丛的亚纯截面层，这些截面层在紧化过程中具有指定的消失级和极级，并包含了它们的同形层。这些包括，例如，层的雅可比形式和弱全纯模形式。使用这种机器，我们给一个简短的和纯粹的代数证明的比例定理的Hirzebruch和芒福德。
英文摘要：
We axiomatize the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalized automorphic sheaf is proposed which includes sheaves of (meromorphic) sections of automorphic vector bundles with prescribed vanishing and pole orders along strata in the compactification, and their quotients. These include, for instance, sheaves of Jacobi forms and weakly holomorphic modular forms. Using this machinery we give a short and purely algebraic proof of the proportionality theorem of Hirzebruch and Mumford.
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