Derived algebraic bordism

General Introduction
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Online References
arXiv:1211.7023 Derived algebraic bordism fra arXiv Front: math.AG av Parker Lowrey, Timo Schürg We study virtual fundamental classes as orientations for quasismooth morphisms of derived schemes. To study these orientations, we introduce BorelMoore functors on quasiprojective derived schemes that have pullbacks for quasismooth morphisms. We construct the universal example of such a theory: derived algebraic bordism. We show quasismooth pullbacks exist for algebraic bordism, the theory developed by Levine and Morel and obtain a natural transformation from algebraic bordism to derived algebraic bordism. We then prove a GrothendieckRiemannRoch type result about the compatibility of pullbacks in both theories. As a consequence we obtain an algebraic version of Spivak's theorem, stating that algebraic bordism and derived algebraic bordism are in fact isomorphic.
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
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