Computations in Stable Motivic Homotopy Theory.

[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.

[发布机构] University of Michigan

[效力级别] Stable Homotopy

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