Algebraic geometry and representation theory in the Verlinde category

This thesis studies algebraic geometry and the representation theory of group schemes in the setting of symmetric tensor categories over algebraically closed fields of positive characteristic. A specific focus is paid to the Verlinde category, a symmetric fusion category in characteristic p that serves as a universal base for all such categories. Symmetric tensor categories provide a natural setting in which it makes sense to discuss the notion of a commutative, associative unital algebra. In the first third of the thesis, we prove some fundamental facts about these algebras, showing that, in the Verlinde category and any category built out of it, finitely generated algebras are Noetherian, have finitely generated invariants and are finite as a module over their invariants. Subsequently, we use this result to extend some fundamental properties of commutative algebras from the original setting of vector spaces to the more general setting of symmetric tensor categories.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2019

Author dc:creator

• Venkatesh, Siddharth(Siddharth Narayan)

Advisor dc:contributor.advisor

• Pavel Etingof.

• Mathematics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/122170

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/122170