Explicit Reciprocity Laws for Higher Local Fields

Author

Jorge Florez, The Graduate Center, City University of New YorkFollow

Date of Degree

9-2016

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Victor Kolyvagin

Advisor

Victor Kolyvagin

Committee Members

Victor Kolyvagin

Kenneth Kramer

Carlos Moreno

Subject Categories

Number Theory

Keywords

Formal groups, class field theory, higher local fields

Abstract

In this thesis we generalize to higher dimensional local fields the explicit reciprocity laws of Kolyvagin for the Kummer pairing associated to a formal group. The formulas obtained describe the values of the pairing in terms of multidimensional p-adic differentiation, the logarithm of the formal group, the generalized trace and the norm on Milnor K-groups.

Recommended Citation

Florez, Jorge, "Explicit Reciprocity Laws for Higher Local Fields" (2016). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/1469