Algebraic cobordism of bundles on varieties. (English) Zbl 1348.14107

This paper considers a notion of algebraic cobordism for vector bundles on varieties, arising from the double point relation. The authors show this theory to be an extension by scalars of the standard algebraic cobordism. Additionally, they exhibit combinatorial \(\mathbb{Q}\)-bases of the cobordism groups associated with the former theory.


14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
55N22 Bordism and cobordism theories and formal group laws in algebraic topology
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