Studies in K-theory and arithmetic

University Of Utah, Salt Lake City UT

Investigators

Abstract

The Principal Investigator will continue her work on two (related) projects. The first project is a culmination of her work on the motivic aspects of p-adic period morphisms. So far she was able to give motivic proofs of the Crystalline and Semi-stable Conjectures: the two main theorems in the theory of p-adic periods. She plans to finish her work on this subject by giving motivic proofs of the de Rham and the Hodge-Tate Conjectures as well as treat the open varieties and compare the three existing period maps. In the second project she proposes to continue studying the log-K-theory groups of log-schemes she has introduced recently as well as regulator maps into log-crystalline and log-etale cohomologies and the monodromy and weight filtrations. The research described in this proposal lies in the field of arithmetic algebraic geometry. This subject aims at solving number theoretical questions via geometric methods as well as at relating arithmetic and geometric phenomena. In the last decades it has been very successful in solving long-standing conjectures, opening new research directions and creating applications in fields as diverse as physics, robotics, data processing and information theory.