# Coherent completeness and the local structure of algebraic stacks

Formal GAGA is an important theorem in formal geometry which categorizes coherent sheaves on a scheme proper over a complete local noetherian ring in terms of compatible families of coherent sheaves on the thickenings of its central fiber. We will discuss generalizations of this result to algebraic stacks and explain how such results can be used to prove local structure theorems for algebraic stacks. After reviewing joint work with Hall and Rydh which establishes a satisfactory result in characteristic 0, we will discuss partial progress in joint work with Hall and Lim on extending this result to positive characteristic.

The discussion for Jarod Alper’s talk is taking place not in zoom-chat, but at https://tinyurl.com/2020-10-23-ja (and will be deleted after ~3-7 days).