Varieties of CM-type

Details Varieties of CM-type Varieties of CM-type

1995-12-05

arxiv.org/abs/alg-geom/9512004v2

Mathematics

Algebraic Geometry

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Scientific paper

We introduce the notion of a variety (or more generally a motive) of CM-type which generalises the well known notion of abelian variety of CM-type. Just as in that particular case it will turn out that the cohomology of the variety is determined by purely combinatorial data; the type of the variety. As applications we will show that the \l-adic representations are given by algebraic Hecke characters whose algebraic parts are determined by the type and give a method for computing the discriminant of the N\'eron-Severi group of super-singular Fermat surfaces.

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