2019/10/15 by Amnon Besser, Besser, Amnon, Wayne Raskind +1
Mathematics · #19F27 (primary) 14G20 (secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1910.06877
openalex publication_date 2019/10/15 · openalex created_date 2022/09/16 · openalex updated_date 2026/07/28
Let X be a variety defined over a local field K of mixed characteristic (0,p) with a totally degenerate reduction in the sense of Raskind and Xarles. Generalizing earlier work of Raskind and Xarles and relying on some conjectures we define a map, which we call the toric regulator, from the various motivic cohomology groups of X to certain p-adically uniformized tori over K. This construction captures the part of the étale regulators on X that land in the Galois cohomology of the submodules of cohomology which are extensions of ℤl by ℤl(1), simultaneously for all l. We also discuss the relation with the log-syntomic regulator and study a number of examples. In particular, for K2 of a Mumford curve we find a relation with the rigid analytic regulator of Pal and for K1 of the product of Mumford curves we conjecture a formula for the toric regulator.