On Anabelian Geometry of Mixed Characteristic Local Fields

• Author / Creator

  Ge, Qi

• The aim of this thesis is to provide an exposition to Mochizuki and Hoshi's approach to birational anabelian geometry of mixed characteristic local fields.
  In the introductory chapter, we begin by recalling the relevant backgrounds on the Grothendieck conjectures on the étale fundamental groups and their morphisms.
  Next, we review mixed characteristic local fields and their local class field theory.
  This leads us to derive that many invariants of a mixed characteristic local field can be reconstructed from its Galois group, but not the field itself.
  We then set out to demonstrate that isomorphisms between mixed characteristic local fields, which preserve certain arithmetic structures such as the ramification filtration or the class of Hodge-Tate representation, are induced by isomorphisms between the fields.
  We provide technical facts on Galois representations in support of this argument.

• Subjects / Keywords

  • Mathematics
  • Geometry
  • Arithmetic
  • Galois Groups
  • Anabelian Geometry

• Graduation date

  Fall 2023

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-z0cp-h295

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.