Dissertation/Thesis Abstract

Line Bundles of Rational Degree Over Perfectoid Space
by Bedi, Harpreet Singh, Ph.D., The George Washington University, 2018, 100; 10681242
Abstract (Summary)

In this thesis we lay the foundation for rational degree d as an element of Z[1/p] by using perfectoid analogue of projective space, and consider power series instead of polynomials. We start the groundwork by proving Weierstrass theorems for perfectoid spaces which are analogues of standard Weierstrass theorems in complex analysis. We then move onto defining sheaves for Projective perfectoid analogue and prove perfectoid analogues of Gorthendieck's classication theorem on projective line, Serre's theorem on Cohomology of line bundles. As intermediate results we also compute Picard groups and describe Cartier and Weil divisors for Perfectoid.

Indexing (document details)
Advisor: Rong, Yongwu, Przytycki, Jozef H.
Commitee: Harizanov, Valentina S., Kedlaya, Kiran S., Ramachandran, Niranjan, Shumakovitch, Alexander, Zhao, Yanxiang
School: The George Washington University
Department: Mathematics
School Location: United States -- District of Columbia
Source: DAI-B 79/04(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Cohomology, Line bundles, Perfectoid
Publication Number: 10681242
ISBN: 978-0-355-54948-5
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