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Texas A&M University
Mathematics

Geometry Seminar

Date: October 18, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Paulo Lima-Filho, Texas A&M University

  

Title: Transforms of geometric currents under correspondences and regulators for Higher Chow groups.

Abstract: In this talk we show how equidimensional algebraic correspondences between complex algebraic varieties can be used to construct pull-backs and transforms on a class of currents representable by integration. As a main application we exhibit explicit formulas at the level of complexes for a regulator map from the Higher Chow groups of smooth quasi-projective complex algebraic varieties to Deligne-Beilinson cohomology, utilizing the original simplicial description of Higher Chow groups with integral coefficients. The main ingredients come from Suslin's equidimensionality results, which show that suitable complexes of equidimensional correspondences are quasi-isomorphic to Bloch's original complex. We indicate how this can be applied to Voevodsky's motivic complexes and realizations of mixed motives. The GMT constructions may be extended to more general metric spaces, such as rigid analytic spaces. This is joint work with Pedro dos Santos and Robert Hardt.