On the opposite of the category of rings

Details On the opposite of the category of rings On the opposite of the category of rings

2008-06-09

arxiv.org/abs/0806.1476v2

Mathematics

Rings and Algebras

43 pages, added Section 8.1 and some references

Scientific paper

We define a faithful contravariant functor NCSpec from the category of rings to the category of ringed spaces, and show that if R is a commutative ring then NCSpec(R) may be viewed as a completion of Spec(R) in an appropriate sense. We then explain how the spaces NCSpec(R) may be glued, and study quasicoherent sheaves on them. As an example, we compute the category of quasicoherent sheaves on a space constructed from a skew-polynomial ring R by an analogue of the Proj construction.

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