Homology, Homotopy and Applications

Volume 22 (2020)

Number 2

Algebraic cobordism in mixed characteristic

Pages: 91 – 103

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a5


Markus Spitzweck (Mathematics Department, Osnabrück University, Osnabrück, Germany)


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.


algebraic cobordism, mixed characteristic

2010 Mathematics Subject Classification

14F42, 57R90

Received 16 August 2017

Received revised 25 August 2019

Published 25 March 2020