Computations in Stable Motivic Homotopy Theory.

Motivic Homotopy;Stable Homotopy;Adams-Novikov Spectral Sequence;Algebraic K-theory;Algebraic Cobordism;Mathematics;Science;Mathematics

Ormsby, Kyle M.Torres Giese, Enrique ;

University of Michigan

关键词: Motivic Homotopy;    Stable Homotopy;    Adams-Novikov Spectral Sequence;    Algebraic K-theory;    Algebraic Cobordism;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/77824/ormsby_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This thesis is concerned with the application of certain computational methods from stable algebraic topology in motivic homotopy theory over p-adic fields.My main tools are motivic analogues of the Adams and Adams-Novikov spectral sequences.I determine the coefficients of 2-complete algebraic cobordism and a type of connective algebraic K-theory in the motivic setting.I describe the E_2-term of the motivic Adams-Novikov spectral sequence in terms of the E_2-term of the topological Adams-Novikov spectral sequence and basic arithmetic information.Within this algebra, I discover a motivic analogue of the alpha family and determine its behavior within the motivic Adams-Novikov spectral sequence.This is an ``infinite result;; in the stable motivic homotopy groups of the 2-complete sphere spectrum over a p-adic field.