Generalized Albanese morphisms
نویسندگان
چکیده
منابع مشابه
Generalized Albanese morphisms
We define generalizations of the Albanese variety for a projective variety X. The generalized Albanese morphisms X albr // _ _ _ Albr(X) contract those curves C in X for which the induced morphism Hom(π1(X),U(r)) → Hom(π1(C),U(r)) has a finite image. Thus, they may be interpreted as a U(r)-version of the Shafarevich morphism.
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Using sheaf theoretic methods, we define functors Lπ0 : DMeff(k) → D(HI≤0(k)) and LAlb : DMeff(k) → D(HI≤1(k)). The functor LAlb extends the one in [3] to nonnecessarily geometric motives. These functors are then used to define higher Néron-Severi groups and higher Albanese sheaves.
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2006
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x05001831