The Category of 1-motivic Sheaves and an Algebraic Avatar of Deligne Cohomology
نویسنده
چکیده
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. The latter may be considered as an algebraic avatar of Deligne (co)homology.
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