The spectrum of prime ideals in tensor triangulated categories
| dc.creator | Balmer, Paul | |
| dc.date | 2004-09-20 | |
| dc.date | 2004-09-22 | |
| dc.date.accessioned | 2026-07-07T05:12:21Z | |
| dc.date.available | 2026-07-07T05:12:21Z | |
| dc.description | 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. | |
| dc.description | 17 pages, short section on structure sheaves added | |
| dc.identifier | https://arxiv.org/abs/math/0409360 | |
| dc.identifier | http://arxiv.org/abs/math/0409360 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72543 | |
| dc.subject | Category Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.subject | 18E30; 14A20; 20C99 | |
| dc.title | The spectrum of prime ideals in tensor triangulated categories | |
| dc.type | text |