Arithmetic Compactifications of PEL-Type Shimura Varieties by Kai-Wen Lan

By Kai-Wen Lan

By learning the degeneration of abelian types with PEL constructions, this ebook explains the compactifications of soft indispensable types of all PEL-type Shimura kinds, supplying the logical beginning for numerous fascinating fresh advancements. The booklet is designed to be available to graduate scholars who've an realizing of schemes and abelian varieties.

PEL-type Shimura types, that are normal generalizations of modular curves, are important for learning the mathematics homes of automorphic kinds and automorphic representations, they usually have performed very important roles within the improvement of the Langlands software. As with modular curves, it's fascinating to have imperative versions of compactifications of PEL-type Shimura kinds that may be defined in adequate aspect close to the boundary. This booklet explains intimately the next themes approximately PEL-type Shimura kinds and their compactifications:

  • A development of tender crucial types of PEL-type Shimura forms by way of defining and representing moduli difficulties of abelian schemes with PEL constructions
  • An research of the degeneration of abelian kinds with PEL buildings into semiabelian schemes, over noetherian general entire adic base jewelry
  • A development of toroidal and minimum compactifications of tender vital types of PEL-type Shimura types, with designated descriptions in their constitution close to the boundary

Through those subject matters, the publication generalizes the idea of degenerations of polarized abelian types and the applying of that idea to the development of toroidal and minimum compactifications of Siegel moduli schemes over the integers (as constructed via Mumford, Faltings, and Chai).

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