The Ziegler spectrum of a derived-discrete algebra

Rosie Laking (Manchester)

Frank Adams 1,

The Ziegler spectrum is a topological space that was first introduced by M. Ziegler in the context of the model theory of modules.  Surprisingly, the definition of the space has an entirely algebraic description, and its structure enables us to study interactions between finite-dimensional and infinite-dimensional objects.  We will introduce the Ziegler spectrum of a (compactly generated) triangulated category, as well as two dimensions on the space.  We will then use the class of derived-discrete algebras to illustrate how the complexity measured by these dimensions is reflected in the structure of the bounded derived category.

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