课程名称：

Introduction to Coherent Functors

授课人：

Ivo Herzog, The Ohio State University

授课方式：Zoom

课程安排：

授课人简介：

Ivo Herzog教授工作于俄亥俄州立大学。他的研究兴趣包括同调代数和代数表示论，逻辑特别是模型理论在代数研究中的应用，以及函子范畴。2015年2月至7月，曾作为富布莱特杰出讲席教授工作于捷克布拉格查理大学，2018年在第十八届代数表示论国际会议(18^th International Conference on Representations of Algebras)做大会报告。迄今为止，他已经在Adv. Math.，Trans. AMS，Proc. LMS， Selecta Math.，Doc. Math., J. Algebra， J. Pure and Applied Algebra等杂志发表39篇论文。

课程内容简介：

Abstract: Auslander's theory of coherent functors offers a functor categorical way to study the representation theory of rings and algebras. There are three ways to describe the category of coherent functors, and in this series of talks we will describe the three styles of argumentation used by these three approaches. The series of lectures will be in 5 parts:

I Definition. Finitely presented modules, representable functors, coherent objects.

II Purity. Pure exact sequences, algebraically compact representations, the Ziegler spectrum.

III Duality. The free abelian category, positive primitive formulae, Auslander-Gruson-Jensen duality.

IV. Examples. Coherent rings, von Neumann regular rings, artin algebras.

V. Recollements of purity. The contravariant, projective quotient and covariant recollements of functor categories.