Homological aspects of perfect algebras
Commutative Algebra
2017-11-16 v5
Abstract
We investigate homological properties of perfect algebras of prime characteristic. The principle is as follows: perfect algebras resolve the singularities. For example, we show any module over the ring of absolute integral closure has finite flat dimension. Under some mild conditions, we show any module over that ring has finite projective dimension. We compute weak dimension and global dimension of perfect rings in a series of nontrivial cases. Some interesting applications are given. In particular, we answer some questions asked by Shimomoto.
Keywords
Cite
@article{arxiv.1005.1462,
title = {Homological aspects of perfect algebras},
author = {Mohsen Asgharzadeh},
journal= {arXiv preprint arXiv:1005.1462},
year = {2017}
}