Immaculate complexes and strong generation by injectives

Isambard Goodbody (University of Glasgow)

Tuesday 20th May 15:00-16:00
Maths 110

Abstract

Strong generation of the derived category can be used to extract properties of a geometric object. Many results of Neeman, Orlov, Rouquier and others support this. For example, Neeman showed the perfect complexes over a Noetherian separated scheme admit a strong generator if and only if it is regular of finite dimension. 

 

We define the immaculate complexes over a Noetherian scheme as the bounded complexes of finite sums of indecomposable injectives. We show that a Noetherian scheme is regular and of finite dimension if and only if the immaculates are strongly generated by the indecomposable injectives.

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