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Motivic cohomology spectral sequence and Steenrod operations
- Part of
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- Journal:
- Compositio Mathematica / Volume 152 / Issue 10 / October 2016
- Published online by Cambridge University Press:
- 24 June 2016, pp. 2113-2133
- Print publication:
- October 2016
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- Article
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For a prime number
$p$ , we show that differentials 
$d_{n}$ in the motivic cohomology spectral sequence with 
$p$ -local coefficients vanish unless 
$p-1$ divides 
$n-1$ . We obtain an explicit formula for the first non-trivial differential 
$d_{p}$ , expressing it in terms of motivic Steenrod 
$p$ -power operations and Bockstein maps. To this end, we compute the algebra of operations of weight 
$p-1$ with 
$p$ -local coefficients. Finally, we construct examples of varieties having non-trivial differentials 
$d_{p}$ in their motivic cohomology spectral sequences.
