University of Illinois Chicago
Browse

The Absolute Integral Closure in Equicharacteristic Zero

Download (535.07 kB)
thesis
posted on 2024-08-01, 00:00 authored by Shravan Patankar
Thesis thesis establishes basic properties of and answers a series of natural questions about the absolute integral closure in equicharacteristic zero. Two main results are summarized as follows. First, we show that it is not coherent as a ring, implying the corresponding statement in mixed characteristic answering an explicit question of Asgharzadeh. Second, we show that the vanishing of tors of characterizes regularity (in graded dimension 2) answering a question of Bhatt, Iyengar, and Ma and also showing that their "theorem", at the time of publication, had vacuous hypothesis. These give new perspectives and questions on corresponding known results in positive and mixed characteristics.

History

Advisor

Kevin Tucker

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois Chicago

Degree Level

  • Doctoral

Degree name

Doctor of Philosophy

Committee Member

I z z e t C o s k u n , L a w r e n c e E i n , W e n l i a n g Z h a n g , K a z u m a S h i m o m o t o

Thesis type

application/pdf

Usage metrics

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC