The spectrum of prime ideals in tensor triangulated categories

@inproceedings{Balmer2004TheSO,
  title={The spectrum of prime ideals in tensor triangulated categories},
  author={Paul Balmer},
  year={2004}
}
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 or some quasi-compactness. Locally trivial morphisms are proved to be… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 102 CITATIONS

Prime spectra of abelian 2-categories and categorifications of Richardson varieties

VIEW 10 EXCERPTS
CITES METHODS, BACKGROUND & RESULTS
HIGHLY INFLUENCED

Recovering Quivers from Derived Quiver Representations

VIEW 6 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Triangular spectrum of some triangulated categories

VIEW 10 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Endotrivial modules for finite group schemes

VIEW 5 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

DESCENT AND NILPOTENCE IN ALGEBRAIC K-THEORY

VIEW 3 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

FILTER CITATIONS BY YEAR

2006
2019

CITATION STATISTICS

  • 22 Highly Influenced Citations

  • Averaged 11 Citations per year from 2017 through 2019

References

Publications referenced by this paper.
SHOWING 1-10 OF 19 REFERENCES

Pevtsova, P-supports for modules for finite groups schemes over a field, preprint 2004. 167 Balmer, The spectrum of tensor triangulated categories

J. E. Friedlander
  • 2004
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Spectra related with localizations, preprint MPIM2003-112 (and more on the Max-Planck preprint server in Bonn)

A. Rosenberg
  • 2003
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL