Noncommutative tensor triangular geometry

Gluing in Tensor Triangular Geometry

We discuss gluing of objects and gluing of morphisms in tensor triangulated categories. We illustrate the results by producing, among other things, a Mayer-Vietoris exact sequence involving Picard groups.

Noncommutative geometry

Tensor Triangular Chow Groups

We propose a definition of the Chow group of a rigid tensor triangulated category. The basic idea is to allow “generalized” cycles, with nonintegral coefficients. The precise choice of relations is open to some fine-tuning. Hypothesis 1. Let K be an essentially small tensor triangulated category. Let us assume that its triangular spectrum in the sense of [1], Spc(K) = { P ⊂ K ∣∣P is prime}, is ...

Gravity From Noncommutative Geometry

We introduce the linear connection in the noncommutative geometry model of the product of continuous manifold and the discrete space of two points. We discuss its metric properties, de ne the metric connection and calculate the curvature. We de ne also the Ricci tensor and the scalar curvature. We nd that the latter di ers from the standard scalar curvature of the manifold by a term, which migh...

Noncommutative Geometry for Pedestrians∗

A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An extensive bibliography has been added containing reference to recent review articles as well as to part of the original literature. LMU-TPW 99-11 ∗Lecure given...