The Equivalence of Grayson and Friedlander-Suslin Spectral Sequences

TL;DR

This thesis proves the equivalence of Grayson and Friedlander-Suslin spectral sequences by developing new techniques involving K_0-presheaves of spectra and constructing filtrations on K-theory presheaves.

Contribution

It introduces novel methods for comparing spectral sequences through filtrations on K-theory presheaves, extending known results from E_2-terms to full spectral sequence equivalence.

Findings

Established the full equivalence of the spectral sequences.

Developed techniques for filtrations on K-theory presheaves.

Extended previous partial results to complete spectral sequence comparison.

Abstract

This thesis establishes the equivalence of Grayson and Friedlander-Suslin spectral sequences, that was previously only known for the respective E_2-terms. We develop the necessary techniques regarding K_0-presheaves of spectra, building on the work of M. Walker and construct certain filtrations on the K-theory presheaf of spectra that we use as intermediate steps in obtaining the equivalence of the filtrations.