We compute the geometric part of algebraic cobordism over Dedekind domains of mixed characteristic after inverting the positive residue characteristics and prove cases of a Conjecture of Voevodsky relating this geometric part to the Lazard ring for regular local bases. The method is by analyzing the slice tower of algebraic cobordism, relying on the Hopkins-Morel isomorphism from the quotient of the algebraic cobordism spectrum by the generators of the Lazard ring to the motivic Eilenberg-MacLane spectrum, again after inverting the positive residue characteristics.

中文翻译：

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混合特征中的代数坐标

我们在反转正残差特征后，计算混合特征 Dedekind 域上代数协边的几何部分，并证明了 Voevodsky 猜想的情况，该猜想将此几何部分与常规局部基的 Lazard 环相关联。该方法是通过分析代数共边的切片塔，依靠霍普金斯-莫雷尔同构从拉扎德环的生成器的代数共边谱的商到动机的Eilenberg-MacLane谱，在反演正残差特征后再次。