Daniel McCormick: Ghost Maps and André-Quillen Homology

Abstract.

A map in the derived category is ghost if it induces the zero map on homology. Ghost maps play an important role in understanding the homological behavior of modules. In this talk, we shift our perspective to commutative ring homomorphisms and introduce an analogous class of maps to this setting. The frobenius endomorphism will be a primary example of a ghost map. We begin with an overview of the necessary tools for handling derived functors in the category of rings, and use this framework to define ghost maps. We conclude with an analog of the ghost lemma in this setting and discuss applications to the study of singularities.