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On the Construction of Higher étale Regulators

Citation

Fan, Sin Tsun Edward (2015) On the Construction of Higher étale Regulators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9BZ63Z1. http://resolver.caltech.edu/CaltechTHESIS:05182015-134458833

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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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:etale motivic cohomoology, etale regulator, Deligne cohomology, vanishing theorems
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Flach, Matthias
Thesis Committee:
  • Flach, Matthias (chair)
  • Ramakrishnan, Dinakar
  • Mantovan, Elena
  • Graber, Thomas B.
Defense Date:13 March 2015
Non-Caltech Author Email:edwardfan1 (AT) gmail.com
Record Number:CaltechTHESIS:05182015-134458833
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:05182015-134458833
DOI:10.7907/Z9BZ63Z1
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8863
Collection:CaltechTHESIS
Deposited By: Sin Tsun Edward Fan
Deposited On:26 May 2015 21:17
Last Modified:29 Jan 2016 15:17

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