2016/04/16 by Fei Sun, Sun, Fei
Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1604.04700
openalex publication_date 2016/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we calculate the differential d1 of the rank spectral sequence. We generalize Quillen's spectral sequence from Dedekind domain to general integral Noetherian ring A by considering the Q-construction Qtf(A) of the category of finitely generated torsion-free modules. In particular, by resolution theorem, if A is regular, then Qtf(A) is homotopy equivalent to QP(A) where P(A) is the category of finitely generated projective A-modules. We deduce the differential d1 by using Tits buildings, Steinberg modules, and modular symbols in the sense of Ash-Rudolph. The spirit of Quillen's categorical homotopy theory will be used intensively throughout this paper.