Diploma Thesis
Pawel Sosna
Tensor Triangulated Categories in Algebraic Geometry
Since 16 May 2007
Advisor: Prof. Dr. Klaus Altmann
We use a tensor structure on a triangulated category to turn the Grothendieck group into a ring and characterize all dense "subrings'' of the triangulated category by subrings of the Grothendieck ring. Further, we apply the spectrum construction to study the connection between the number of Fourier-Mukai partners of a given scheme and the number of tensor structures on its derived category. In the last chapter we compute the spectra of some tensor triangulated categories which arise in algebraic geometry.
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