Citation
Fan, Sin Tsun Edward (2015) On the Construction of Higher étale Regulators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9BZ63Z1. https://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.)) |
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| 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) |
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| Thesis Committee: |
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| Defense Date: | 13 March 2015 |
| Non-Caltech Author Email: | edwardfan1 (AT) gmail.com |
| Record Number: | CaltechTHESIS:05182015-134458833 |
| Persistent URL: | https://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: | 04 Oct 2019 00:07 |
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