Homotopy Invariant Commutative Algebra over fields

TL;DR

This paper discusses the application of homotopy invariant methods in commutative algebra, extending classical concepts to derived categories of rings and ring spectra, with broad implications across algebra and topology.

Contribution

It introduces a homotopy invariant framework for commutative algebra applicable to derived categories and ring spectra, enhancing classical and modern algebraic techniques.

Findings

Homotopy invariant formulations unify various algebraic theories.

Applications demonstrated in derived categories and ring spectra.

Potential to influence algebraic topology and representation theory.

Abstract

These notes illustrates the power of formulating ideas of commutative algebra in a homotopy invariant form. They can then be applied to derived categories of rings or ring spectra. These ideas are powerful in classical algebra, in representation theory of groups, in classical algebraic topology and elsewhere. The notes grew out of a series of lectures given during the `Interactions between Representation Theory, Algebraic Topology and Commutative Algebra' (IRTATCA) at the CRM (Barcelona) in Spring 2015.