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The Coniveau Filtration on
$\text{K}_{1}$ for Some Severi–Brauer Varieties
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 3 / September 2019
- Published online by Cambridge University Press:
- 24 October 2018, pp. 565-576
- Print publication:
- September 2019
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- Article
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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 
$i>0$.
Motivic cohomology of quadrics and the coniveau spectral sequence
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- Journal:
- Journal of K-Theory / Volume 6 / Issue 3 / December 2010
- Published online by Cambridge University Press:
- 05 November 2010, pp. 547-589
- Print publication:
- December 2010
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We study the coniveau spectral sequence for quadrics defined by Pfister forms. In particular, we explicitly compute the motivic cohomology of anisotropic quadrics over ℝ, by showing that their coniveau spectral sequences collapse from the
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