Notes on Grothendieck topologies, fibered categories and descent theory

TL;DR

This paper introduces Grothendieck's descent theory, emphasizing the machinery of fibered categories and stacks to facilitate understanding of descent in algebraic geometry.

Contribution

It provides an accessible introduction to descent theory, fibered categories, and stacks, highlighting their interrelations and foundational role in algebraic geometry.

Findings

Clarifies the role of fibered categories in descent theory

Explains the concept of stacks in the context of Grothendieck topologies

Provides foundational insights into the machinery underlying descent

Abstract

This is an introduction to Grothendieck's descent theory, with some stress on the general machinery of fibered categories and stacks.