SFU Number Theory and Algebraic Geometry Seminar: Nathan Ilten

Abstract: The cotangent cohomology modules $T_S^i$ for a commutative algebra $S$ over a field $k$ provide important homological and deformation-theoretic information about $S$, but are often challenging to describe explicitly. In this talk, I will focus on the case when $S$ is a Stanley-Reisner ring, i.e. the quotient of a polynomial ring by a radical monomial ideal $I$. In this setting, Altmann and Christophersen gave combinatorial descriptions of $T_S^i$ for $i\leq 2$. I will report on joint work with Francesco Meazzini and Andrea Petracci, in which we partially generalize Altmann and Christophersen's results to higher cotangent cohomology (i.e. $i\geq 3$). No prior background in cotangent cohomology or Stanley-Reisner rings is assumed.