The Grothendieck ring of varieties, and stabilization in the algebro-geometric setting - part 1 of 2

A central theme of this workshop is the fact that arithmetic and topological structures become best behaved “in the limit”. The Grothendieck ring of varieties (or stacks) gives an algebro-geometric means of discovering, proving, or suggesting such phenomena

In the first lecture of this minicourse, Ravi Vakil will introduce the ring, and describe how it can be used to prove or suggest such stabilization in several settings.

This is the first lecture in a two part series: part 2

In the second lecture of the minicourse, Aaron Landesman will use these ideas to describe a stability of the space of low degree covers (up to degree 5) of the projective line (joint work with Vakil and Wood). The results are cognate to Bhargava’s number field counts, the philosophy of Ellenberg-Venkatesh-Westerland, and Anand Patel’s fever dream.