## A moving lemma for relative 0-cycles.(English)Zbl 1440.14036

Summary: We prove a moving lemma for the additive and ordinary higher Chow groups of relative $$0$$-cycles of regular semilocal $$k$$-schemes essentially of finite type over an infinite perfect field. From this, we show that the cycle classes can be represented by cycles that possess certain finiteness, surjectivity, and smoothness properties. It plays a key role in showing that the crystalline cohomology of smooth varieties can be expressed in terms of algebraic cycles.

### MSC:

 14C25 Algebraic cycles 14F42 Motivic cohomology; motivic homotopy theory 19E15 Algebraic cycles and motivic cohomology ($$K$$-theoretic aspects)
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### References:

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