Title: The mod (p,v_1) K-theory of Z/p^n
Speaker: Andrew Senger
Speaker Info: Harvard University
While Z/p^n is a relatively simple ring, its algebraic K-theory groups are very complicated, and their computation has been an open problem for many years. Recently, prismatic methods have made the computation of these groups a purely algebraic question, and Antieau--Krause--Nikolaus have leveraged this to (among other results) write a computer program which can compute K_* (Z/p^n) in a range of stems.Date: Monday, October 09, 2023
In this talk, I will describe a different approach to the computation of K_* (Z/p^n). Instead of computing the groups in a range, we completely compute the mod (p,v_1) algebraic K-theory pi_* K (Z/p^n)/(p,v_1), which is substantially simpler. Time permitting, I will share some hopes and results about the v_1-Bockstein spectral sequence converging to pi_* K (Z/p^n)/p.
This is joint work with Jeremy Hahn and Ishan Levy.