The spectrum of prime ideals in tensor triangulated categories

Details The spectrum of prime ideals in tensor triangulated categories The spectrum of prime ideals in tensor triangulated categories

2004-09-20

arxiv.org/abs/math/0409360v2

Mathematics

Category Theory

17 pages, short section on structure sheaves added

Scientific paper

We define the spectrum of a tensor triangulated category $K$ as the set of so-called prime ideals, endowed with a suitable topology. In this very generality, the spectrum is the universal space in which one can define supports for objects of $K$. This construction is functorial with respect to all tensor triangulated functors. Several elementary properties of schemes hold for such spaces, e.g. the existence of generic points and some quasi-compactness. Locally trivial morphisms are proved to be nilpotent. We establish in complete generality a classification of thick tensor-ideal subcategories in terms of arbitrary unions of closed subsets with quasi-compact complements (Thomason's theorem for schemes, mutatis mutandis). We also equip this spectrum with a sheaf of rings, turning it into a locally ringed space. We compute examples and show that our spectrum unifies the schemes of algebraic geometry and the support varieties of modular representation theory.

Affiliated with

Also associated with

No associations

Rating

The spectrum of prime ideals in tensor triangulated categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The spectrum of prime ideals in tensor triangulated categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The spectrum of prime ideals in tensor triangulated categories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-42282