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arXiv · 2108.13563

Motivic cohomology of fat points in Milnor range via formal and rigid geometries

Jinhyun Park
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Abstract

We present a formal scheme based cycle model for the motivic cohomology of the fat points defined by the truncated polynomial rings $k[t]/(t^m)$ with $m \geq 2$, in one variable over a field $k$. We compute their Milnor range cycle class groups when the field has sufficiently many elements. With some aids from rigid analytic geometry and the Gersten conjecture for the Milnor $K$-theory resolved by M. Kerz, we prove that the resulting cycle class groups are isomorphic to the Milnor $K$-groups of the truncated polynomial rings, generalizing a theorem of Nesterenko-Suslin and Totaro.

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Jinhyun Park. 2021-08-31. Motivic cohomology of fat points in Milnor range via formal and rigid geometries. https://arxiv.org/abs/2108.13563

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