## Topological and Geometric aspects of the Ziegler Spectrum (1998)

Citations: | 7 - 5 self |

### BibTeX

@MISC{Prest98topologicaland,

author = {Mike Prest},

title = {Topological and Geometric aspects of the Ziegler Spectrum},

year = {1998}

}

### OpenURL

### Abstract

The aim here is to emphasise the topological and geometric structure that the Ziegler spectrum carries and to illustrate how this structure may be used in the analysis of particular examples. There is not space here for me to give a survey of what is known about the Ziegler spectrum so there are a number of topics that I will just mention in order to give some indication of what lies beyond what is discussed here. 1. The Ziegler spectrum 2. Various dimensions 3. These dimensions for artin algebras 4. These dimensions in general 5. Duality 6. The complexity of morphisms in mod-R 7. The Gabriel-Zariski topology 8. The sheaf of locally definable scalars 1 The Ziegler spectrum 1.1 A reminder on purity and pure-injectives Suppose that M is a submodule of N . Consider a finite system \Sigma n i=1 x i r ij = a j (j = 1; :::m) of R-linear equations over M : that is, the r ij are in R, the 1 a j are in M and the x i are indeterminates. Suppose that there is a solution b 1 ; ...