Lectures on Large Stable Fields

Dave Marker

Spring 2021


I will give a weekly series of lectures leading up to the new result of Johnson, Tran, Walsberg and Ye that large stable fields are separably closed. Lectures will be Mondays at 4:00pm beginning Monday January 25.

A long outstanding conjecture is that every infinite stable field is separably closed. The class of large fields was introduced in field arithmetic and includes all of the known examples of fields where there is a reasonable model theory.

I will begin with an introduction to stable groups, discuss earlier work done on stable fields and review the necessary background on large fields.

I plan to give one lecture/week on Zoom, Each session will be at most 75 minutes, but more likely an hour or less. Please contact me (marker@uic.edu) if you need the Zoom link.


Ideally students will have seen the basics of stability as presented, say, in Tent-Ziegler, but I will try to review all the results I'm using.

The chapter of my text on omega-stable groups is also useful background.


Lecture Notes

Last Revised: 3/15/21