2002•Hindustan Book AgencyRequires access

Lefschetz Properties of Subvarieties of Shimura Varieties

T. N. Venkataramana

Abstract

We give examples of cycle classes on certain unitary Shimura varieties which are not generated by Hecke translates of classes of Shimura subvarieties. We also give examples of cohomology classes (of low degree) which do not survive on any Shimura subvariety, thereby showing that the span of Hecke translates of Shimura subvarieties can never contain the class of an ample subvariety.

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Key concepts: Subvariety, Shimura variety, Mathematics, Pure mathematics, Unitary state, Class (philosophy), Cohomology, Computer science