Amnon Besser (Ben-Gurion University)
I will present a map - The toric regulator, from motivic cohomology of algebraic varieties over p-adic fileds with "totally degenerate reduction", e.g., $p$-adically uniformized varieties, to "toric intermediate Jacobians" which are quotients of algebraic toruses by a discrete subgroup. The toric regulator recovers part of the $\ell$-adic etale regulator map for every prime $\ell$, and its logarithm recovers part of the log-syntomic regulator. I expect the toric regulator to be the home of "refined" Beilinson conjectures and I will present some evidence for this claim. This is joint work with Wayne Raskind from Wayne State university.