Citation
Siebel, Daniel A. (2019) Special Values of Zeta-Functions for Proper Regular Arithmetic Surfaces. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YMHN-2T74. https://resolver.caltech.edu/CaltechTHESIS:11142018-032432585
Abstract
We explicate Flach's and Morin's special value conjectures in [8] for proper regular arithmetic surfaces π : X → Spec Z and provide explicit formulas for the conjectural vanishing orders and leading Taylor coefficients of the associated arithmetic zeta-functions. In particular, we prove compatibility with the Birch and Swinnerton-Dyer conjecture, which has so far only been known for projective smooth X. Further, we derive a direct sum decomposition of Rπ*Z(n) into motivic degree components.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
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| Subject Keywords: | Special Values, Zeta-Functions, Arithmetic Surface |
| Degree Grantor: | California Institute of Technology |
| Division: | Physics, Mathematics and Astronomy |
| Major Option: | Mathematics |
| Awards: | Apostol Award for Excellence in Teaching in Mathematics, 2015. |
| Thesis Availability: | Public (worldwide access) |
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| Defense Date: | 9 November 2018 |
| Record Number: | CaltechTHESIS:11142018-032432585 |
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:11142018-032432585 |
| DOI: | 10.7907/YMHN-2T74 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 11273 |
| Collection: | CaltechTHESIS |
| Deposited By: | Daniel Siebel |
| Deposited On: | 10 Dec 2018 22:13 |
| Last Modified: | 04 Oct 2019 00:23 |
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