English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Algebraic aspects of noncommutative tori : the Riemann–Hilbert correspondence

Mahanta, S. (2007). Algebraic aspects of noncommutative tori: the Riemann–Hilbert correspondence. PhD Thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn.

Item is

Files

show Files
hide Files
:
Mahanta_Algebraic aspects_2007.pdf (Any fulltext), 621KB
 
File Permalink:
-
Name:
Mahanta_Algebraic aspects_2007.pdf
Description:
-
OA-Status:
Visibility:
Private
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show
hide
Description:
-
OA-Status:

Creators

show
hide
 Creators:
Mahanta, Snigdhayan1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

Content

show
hide
Free keywords: -
 Abstract: In this thesis we have tried to figure out some algebraic aspects of noncommutative tori, aiming at generalizing them to arbitrary noncommutative spaces. In the second section all relevant definitions, some examples and motivations have been provided.
In the third section we look at the example of noncommutative tori and see how they can be related to similar objects called noncommutative elliptic curves. We extract a suitably well-behaved subcategory of the category of holomorphic bundles over noncommutative tori. This category turns out to admit a Tannakian structure with Z+ΘZ as the fundamental group. The key to this construction is an equivariant version of the classical Riemann–Hilbert correspondence. The aim was to construct homotopy theoretic invariants of noncommutative tori, e.g., fundamental groups and we make a proposal to that end.
The last two sections constitute an attempt to rewrite some parts of noncommutative algebraic geometry in the framework of DG categories. We provide a description of the category of noncommutative spaces and their associated noncommutative motives. We had some arithmetic applications in mind, namely, introducing and studying motivic zeta functions of noncommutative tori. We propose a universal motivic measure on the category of noncommutative spaces. In it lies a subcategory consisting of noncommutative Calabi–Yau spaces containing elliptic curves and noncommutative tori. In this setting we introduce a motivic zeta function of noncommutative tori; more generally that of noncommutative Calabi–Yau spaces. Our work should be put in perspective with the Real Multiplication programme of Manin.

Details

show
hide
Language(s): eng - English
 Dates: 2007
 Publication Status: Accepted / In Press
 Pages: [75] p.
 Publishing info: Bonn : Rheinische Friedrich-Wilhelms-Universität Bonn
 Table of Contents: -
 Rev. Type: -
 Identifiers: URN: https://nbn-resolving.org/urn:nbn:de:hbz:5N-11377
 Degree: PhD

Event

show

Legal Case

show

Project information

show

Source

show