Motivic cohomology spectral sequence and Steenrod operations
2016 ◽
Vol 152
(10)
◽
pp. 2113-2133
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Keyword(s):
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.
2011 ◽
Vol 7
(3)
◽
pp. 597-618
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2008 ◽
Vol 8
(1)
◽
pp. 39-97
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2020 ◽
pp. 45-56
1982 ◽
Vol 273
(2)
◽
pp. 737-737
◽
2002 ◽
Vol 35
(6)
◽
pp. 773-875
◽