Algebraic K-Theory and Modular Symbols

Fei Sun

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arXiv · 1604.04700

Algebraic K-Theory and Modular Symbols

Fei Sun

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Abstract

In this paper, we calculate the differential $d^1$ 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 $Q^{tf}(A)$ of the category of finitely generated torsion-free modules. In particular, by resolution theorem, if $A$ is regular, then $Q^{tf}(A)$ is homotopy equivalent to $QP(A)$ where $P(A)$ is the category of finitely generated projective $A$-modules. We deduce the differential $d^1$ 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.

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BibTeX RIS

Fei Sun. 2016-04-16. Algebraic K-Theory and Modular Symbols. https://arxiv.org/abs/1604.04700

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