Park, Jinhyun; Ünver, Sinan

Motivic Cohomology of Fat Points in Milnor Range

Doc. Math. 23, 759-798 (2018)
DOI: 10.25537/dm.2018v23.759-798
Communicated by Thomas Geisser

Summary

We introduce a new algebraic-cycle model for the motivic cohomology theory of truncated polynomials $k[t]/(t^m)$ in one variable. This approach uses ideas from the deformation theory and non-archimedean analysis, and is distinct from the approaches via cycles with modulus. We compute the groups in the Milnor range when the base field is of characteristic 0, and prove that they give the Milnor $K$-groups of $k[t]/(t^m)$, whose relative part is the sum of the absolute Kähler differential forms.

Mathematics Subject Classification

14C25, 19D45, 14D15, 11J61

Keywords/Phrases

algebraic cycle, higher Chow group, motivic cohomology, Milnor $K$-theory

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Affiliation

Park, Jinhyun
Dept. of Mathematical Sciences, Korea Advanced Institute of Science and Technology KAIST, 291 Daehak-ro Yuseong-gu, Daejeon, 34141, Republic of Korea (South)
Ünver, Sinan
Dept. of Mathematics, Koc University, Rumelifeneri Yolu, 34450, Sariyer-Istanbul, Turkey

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