By Kai-Wen Lan
By learning the degeneration of abelian types with PEL constructions, this ebook explains the compactifications of gentle indispensable types of all PEL-type Shimura kinds, supplying the logical starting place for a number of interesting fresh advancements. The publication is designed to be obtainable to graduate scholars who've an knowing of schemes and abelian varieties.
PEL-type Shimura forms, that are normal generalizations of modular curves, are beneficial for learning the mathematics houses of automorphic kinds and automorphic representations, and so they have performed vital roles within the improvement of the Langlands software. As with modular curves, it really is fascinating to have imperative versions of compactifications of PEL-type Shimura forms that may be defined in adequate aspect close to the boundary. This e-book explains intimately the subsequent themes approximately PEL-type Shimura forms and their compactifications:
- A development of tender fundamental types of PEL-type Shimura kinds via defining and representing moduli difficulties of abelian schemes with PEL constructions
- An research of the degeneration of abelian types with PEL buildings into semiabelian schemes, over noetherian general entire adic base jewelry
- A development of toroidal and minimum compactifications of tender essential versions of PEL-type Shimura types, with distinct descriptions in their constitution close to the boundary
Through those subject matters, the booklet generalizes the idea of degenerations of polarized abelian kinds and the appliance of that thought to the development of toroidal and minimum compactifications of Siegel moduli schemes over the integers (as built via Mumford, Faltings, and Chai).
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