Cotangent Cohomology for Matroids

Abstract: The first cotangent cohomology module $T^1$ describes the first order deformations of a commutative ring. For Stanley-Reisner rings, this module has a purely combinatorial description: its multigraded components are given as the relative cohomology of some topological spaces associated to the defining simplicial complex. When the Stanley-Reisner ring is associated to a matroid, I will present a very explicit formula for the dimensions of these components. Furthermore, I will show that $T^1$ provides a new complete characterization for matroids.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: Description: Research/departmental seminar

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