Date of Submission

4-28-2018

Date of Award

4-28-2019

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Mathematics

Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

Supervisor

Das, Mrinal Kanti (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

Let R be a commutative, Noetherian ring of (Krull) dimension d. It is well known that the set of isomorphism classes of (oriented, if d is even) stably free R-modules of rank d carries the structure of an abelian group. This group can be identified with the orbit space of unimodular rows namely, Umd+1(R)/SLd+1(R). The prime objective of this thesis is to provide the complete computation of this group, when X = Spec(R) be a smooth real affine variety of dimension d ≥ 2 (with the assumption that the set of real points of X is non-empty and orientable). In order to achieve our goal, we first carry out the computation of the 00elementary orbit space00 Umd+1(R)/Ed+1(R), when X = Spec(R) be as above. We also prove a structure theorem for the Mennicke symbols of length d + 1 (MSd+1(R)). These results will be discussed in Chapter 4. These results have been obtained in a joint work with Mrinal Kanti Das and Md. Ali Zinna. This thesis is based primarily on our paper [DTZ1].

Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28842751

Control Number

ISILib-TH485

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

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