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Motivic cohomology spectral sequence and Steenrod operations

  • Serge Yagunov (a1) (a2)

Abstract

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.

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Motivic cohomology spectral sequence and Steenrod operations

  • Serge Yagunov (a1) (a2)

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