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- W3190131129 abstract "We construct log-motivic cohomology groups for semistable varieties and study the $p$-adic deformation theory of log-motivic cohomology classes. Our main result is the deformational part of a $p$-adic variational Hodge conjecture for varieties with semistable reduction: a rational log-motivic cohomology class in bidegree $(2r,r)$ lifts to a continuous pro-class if and only if its Hyodo-Kato class lies in the $r$-th step of the Hodge filtration. This generalises a theorem of Bloch-Esnault-Kerz which treats the good reduction case, and a theorem of Yamashita which treats the case $r=1$ (the logarithmic Picard group). Along the way, we relate log-motivic cohomology to logarithmic Milnor $K$-theory and the logarithmic Hyodo-Kato Hodge-Witt sheaves." @default.
- W3190131129 created "2021-08-16" @default.
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- W3190131129 date "2021-08-05" @default.
- W3190131129 modified "2023-09-27" @default.
- W3190131129 title "Motivic cohomology of semistable varieties" @default.
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