Algebraic Cobordism

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The authors present a groundbreaking approach to oriented cohomology theory within the context of smooth varieties over a fixed field, introducing Algebraic Cobordism as a universal theory in characteristic 0. They demonstrate that this theory aligns with Quillen's theorems, revealing that the cobordism of the base field corresponds to the Lazard ring, while smooth varieties are generated by positive degree elements. Additionally, the book addresses the generalized degree formula conjectured by Rost and includes various examples and applications to illustrate the concepts.