posted on 2024-08-01, 00:00authored byShravan 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
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