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The Coniveau Filtration on 
$\text{K}_{1}$ for Some Severi–Brauer Varieties
Published online by Cambridge University Press: 24 October 2018
Abstract
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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 
$i>0$.
MSC classification
Primary:
19E08: $K$-theory of schemes
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- © Canadian Mathematical Society 2018
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