Hochschild homology of rings of algebraic integers
type: Item
instance of: scholarly article
title: Hochschild homology of rings of algebraic integers
zbMATH Open document ID: 0973.13006
DOI: 10.1007/PL00000429
author: Javier Majadas
published in: Archiv der Mathematik
publication date: 2001-11-28T00:00:00Z
review text: In 1970, \textit{D. Quillen} showed how the (now so-called) André-Quillen cotangent complex of a commutative algebra can be used to study its Hochschild homology [see Appl. Categorical Algebra, Proc. Symp. Pure Math. 17, 65-87 (1970; Zbl 0234.18010)]. The main purpose of the paper under review is to remind that the André-Quillen homology theory is a very useful tool to study Hochschild homology of commutative algebras. The author chooses as an example the computation of Hochschild homology of Dedekind extensions. More concretely, if \(R\) is a Dedekind domain with fraction field \(K\), \(L\) is a finite separable field extension of \(K\), \(S\) is the integral closure of \(R\) in \(L\), and all the residue fields of \(R\) are perfect, the author proves that the Hochschild homology \[ HH_n(S/R)= \begin{cases} S,\quad & \text{if }n=0,\\ \Omega_{S/R},\quad & \text{if }n\text{ is odd},\\ 0,\quad &\text{if } n>0\text{ is even}.\end{cases}. \]
reviewed by: Tong Wenting
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13B02
zbMATH DE Number: 1538410
zbMATH Keywords: André-Quillen homology theory
zbMATH Keywords: Hochschild homology
zbMATH Keywords: Dedekind extensions
MaRDI profile type: Publication
full work available at URL: pl00000429
OpenAlex ID: W2084105669
Recommended article: On higher topological Hochschild homology of rings of integers
Recommended article: Topological Hochschild homology of number rings
Recommended article: Q5267485
Recommended article: Hochschild homology and algebraic spaces
Recommended article: Zeroth Hochschild homology of preprojective algebras over the integers
Recommended article: Hochschild homology of structured algebras
Recommended article: Hochschild Cohomology for Algebras
Recommended article: Cyclic homology of some rings of algebraic numbers
Recommended article: Q4206909
Recommended article: Q4854347
description: scientific article; zbMATH DE number 1538410