Date of Submission

3-28-2019

Date of Award

3-28-2020

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

Sreekantan, Ramesh

Abstract (Summary of the Work)

The following formula, usually called Beilinson’s formula — though independently due to Deligne as well — describes the motivic cohomology group of a smooth projective variety X over a number field as the group of extensions in a conjectured abelian category of mixed motives, MMQ.The aim of this thesis is to describe this construction in the case of the motivic cohomology group of the Jacobian of a curve. The first work in this direction is due to Harris [Har83] and Pulte [Pul88], [Hai87]. They showed that the Abel-Jacobi image of the modified diagonal cycle on the triple product of a pointed curve (C, P), or alternatively the Ceresa cycle in the Jacobian Jac(C) of the curve, is the same as an extension class coming from JP /J3 P , where JP is the augmentation ideal in the group ring of the fundamental group of C based at P. In [Col02], Colombo extended this theorem to show that the regulator of a cycle in the motivic cohomology of a Jacobian of a hyperelliptic curve, discovered by Collino [Col97], can be realised as an extension class coming from JP /J4 P , where JP is the augmentation ideal of a related curve. In this thesis we extend Colombo’s result to more general curves.

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:28842747

Control Number

ISILib-TH

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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