2008/10/24 by Karl Rökaeus, Rökaeus, Karl
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.0810.4496
10 pages
arxiv created 2008/10/24 · arxiv updated 2009/12/01
We give a version of geometric motivic integration that specializes to p-adic integration via point counting. This has been done before for stable sets; we extend this to more general sets. The main problem in doing this is that it requires to take limits, hence the measure will have to take values in a completion of the (localized) Grothendieck ring of varieties. The standard choice is to complete with respect to the dimension filtration; however, since the point counting homomorphism is not continuous with respect to this topology we have to use a stronger one. The first part of the paper is devoted to defining this topology; in the second part we will then see that many of the standard constructions of geometric motivic integration work also in this setting.