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

Authors
  • Wildeshaus, J.
Type
Preprint
Publication Date
May 19, 2011
Submission Date
Jun 29, 2007
Identifiers
arXiv ID: 0706.4447
Source
arXiv
License
Yellow
External links

Abstract

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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