Syntomic regulators for K_2 of curves with arbitrary reduction

Algebra Seminar
Monday, January 29, 2018 - 15:00
1 hour (actually 50 minutes)
Georgia Tech/Ben-Gurion University
I will explain how to explicitly compute the syntomic regulator for varieties over $p$-adic fields, recently developed by Nekovar and Niziol, in terms of Vologodsky integration. The formulas are the same as in the good reduction case that I found almost 20 years ago. The two key ingrediants are the understanding of Vologodsky integration in terms of Coleman integration developed in my work with Zerbes and techniques for understanding the log-syntomic regulators for curves with semi-stable reduction in terms of the smooth locus.