Recent advances in Iwasawa theory for non-equal characteristic extensions

Iwasawa theory is a rich area of number theory that studies how arithmetic objects evolve in infinite towers of field extensions. Typically, the focus has been on the p-primary parts of arithmetic objects such as ideal class groups and Selmer groups over extensions built using the same prime p, for instance those generated by p-power roots of unity. But what happens when the primes don’t match? Can we understand the p-primary structure over extensions constructed using a different prime q? This seemingly simple twist opens up an intriguing and less-explored direction. In this talk, I’ll review classical results and share some recent advances in this setting. Along the way, we’ll discuss some new results on a little-known folklore conjecture.
 

Bio
https://www.uottawa.ca/faculty-science/professors/antonio-lei