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The Coniveau Filtration on $\text{K}_{1}$ for Some Severi–Brauer Varieties

Part of: Cycles and subschemes $K$-theory in geometry

Published online by Cambridge University Press:  24 October 2018

Eoin Mackall
Eoin Mackall*
Affiliation:
Mathematical & Statistical Sciences, University of Alberta, Edmonton, AB Email: mackall@ualberta.ca
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Abstract

We produce an isomorphism $E_{\infty }^{m,-m-1}\cong \text{Nrd}_{1}(A^{\otimes m})$ between terms of the $\text{K}$-theory coniveau spectral sequence of a Severi–Brauer variety $X$ associated with a central simple algebra $A$ and a reduced norm group, assuming $A$ has equal index and exponent over all finite extensions of its center and that $\text{SK}_{1}(A^{\otimes i})=1$ for all $i>0$.

Keywords

Severi–Brauer varietyconiveau spectral sequence

MSC classification

Primary: 19E08: $K$-theory of schemes
Secondary: 14C35: Applications of methods of algebraic $K$-theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 3 , September 2019 , pp. 565 - 576
Copyright
© Canadian Mathematical Society 2018 

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