Functor of Points and Descent - Talk 2

Explore advanced mathematical concepts in this seminar talk from the UChicago BunG series, where Justin Campbell delves into the functor of points perspective and descent theory. Begin with a foundational exploration of scheme definitions through the functor of points approach, then advance to more complex topics involving functors valued in groupoids and the emergence of stacks as 2-categorical upgrades of sheaves. Examine illustrative examples demonstrating the limitations of Zariski topology and learn why étale or fppf topology serves as more suitable alternatives. Conclude with an in-depth analysis of various approaches to defining Artin or algebraic stacks and their local isomorphism properties in relation to affine schemes.