Čech cohomology of semiring schemes

Z2-graded Čech Cohomology in Noncommutative Geometry ∗ Do Ngoc Diep

The Z 2-gradedČech cohomology theory is considered in the framework of noncommutative geometry over complex number field and in particular the homotopy invariance and Morita invariance are proven. In some special case we deduce an isomorphism between this noncom-mutative theory and the classical Z 2-gradedČech cohomology theory.

Cohomology of Schemes

Cohomology of Schemes

Cohomology of F1-schemes

1 Belian categories 3 1.1 Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Diagram chase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Snake Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Delta functors . . . . . . . . . . . . . . . . . . . . ....

Semiring-Based Mini-Bucket Partitioning Schemes

Graphical models are one of the most prominent frameworks to model complex systems and efficiently query them. Their underlying algebraic properties are captured by a valuation structure that, most usually, is a semiring. Depending on the semiring of choice, we can capture probabilistic models, constraint networks, cost networks, etc. In this paper we address the partitioning problem which occu...