Pure motives, mixed motives and extensions of motives associated to singular surfaces

Details Pure motives, mixed motives and extensions of motives associated to singular surfaces Pure motives, mixed motives and extensions of motives associated to singular surfaces

2007-06-29

arxiv.org/abs/0706.4447v4

Mathematics

K-Theory and Homology

40 pages; final version

Scientific paper

We first recall the construction of the Chow motive modelling intersection cohomology of a proper surface and study its fundamental properties. Using Voevodsky's category of effective geometrical motives, we then study the motive of the exceptional divisor in a non-singular blow-up. If all geometric irreducible components of the divisor are of genus zero, then Voevodsky's formalism allows us to construct certain one-extensions of Chow motives, as canonical sub-quotients of the motive with compact support of the smooth part of the surface. Specializing to Hilbert--Blumenthal surfaces, we recover a motivic interpretation of a recent construction of A. Caspar.

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