On the Construction of Higher étale Regulators

Author: Fan, Sin Tsun Edward

Year: 2015

Degree: Dissertation (Ph.D.)

Advisor: Flach, Matthias

Committee Members: Flach, Matthias; Ramakrishnan, Dinakar; Mantovan, Elena; Graber, Thomas B.

Option: Mathematics

DOI: 10.7907/Z9BZ63Z1

Abstract

We present three approaches to define the higher étale regulator maps Φr,net : Hret(X,Z(n)) → HrD(X,Z(n)) for regular arithmetic schemes. The first two approaches construct the maps on the cohomology level, while the third construction provides a morphism of complexes of sheaves on the étale site, along with a technical twist that one needs to replace the Deligne-Beilinson cohomology by the analytic Deligne cohomology inspired by the work of Kerr, Lewis, and Müller-Stach. A vanishing statement of infinite divisible torsions under Φr,net is established for r > 2n + 1.

Files