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A Comparison of p-adic Motivic Cohomology and Rigid Cohomology


Lawless Hughes, Nathaniel (2019) A Comparison of p-adic Motivic Cohomology and Rigid Cohomology. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DCJJ-E164.


We study two conjectures introduced by Flach and Morin in [FM18] for schemes over a perfect field of characteristic p > 0. The first conjecture relates a p-adic extension of the étale motivic cohomology with compact support on general schemes introduced by Geisser in [Gei06] to rigid cohomology with compact support, and is proved here. The second, relates a p-adic Borel-Moore motivic homology with the dual of rigid cohomology with compact support, and is proved in the smooth case. For this, we also prove a generalization of the comparison theorem from rigid cohomology to overconvergent de Rham-Witt cohomology in [DLZ11].

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics; number theory; arithmetic geometry; rigid cohomology; motivic cohomology; overconvergent de rham-whit cohomology
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Awards:Apostol Award for Excellence in Teaching in Mathematics, 2016.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Flach, Matthias
Thesis Committee:
  • Mantovan, Elena (chair)
  • Flach, Matthias
  • Ramakrishnan, Dinakar
  • Zhu, Xinwen
Defense Date:24 May 2019
Record Number:CaltechTHESIS:06012019-191035765
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapters V and VI.
Lawless Hughes, Nathaniel0000-0003-2755-4065
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11598
Deposited By: Nathaniel Lawless Hughes
Deposited On:10 Jun 2019 22:24
Last Modified:04 Oct 2019 00:26

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