Abstract
Abstract
We axiomatise the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalised 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.
Publisher
Cambridge University Press (CUP)
Reference18 articles.
1. Arithmetic vector bundles and automorphic forms on Shimura varieties II;Harris;Compositio Math.,1986
2. Smooth Compactifications of Locally Symmetric Varieties, 2nd ed. (Cambridge Mathematical Library, Cambridge University Press, Cambridge, 2010);Ash;With the collaboration of Peter Scholze.
3. Complex analytic connections in fibre bundles