Derived algebraic bordism

General Introduction

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arXiv:1211.7023 Derived algebraic bordism fra arXiv Front: math.AG av Parker Lowrey, Timo Schürg We study virtual fundamental classes as orientations for quasi-smooth morphisms of derived schemes. To study these orientations, we introduce Borel--Moore functors on quasi-projective derived schemes that have pull-backs for quasi-smooth morphisms. We construct the universal example of such a theory: derived algebraic bordism. We show quasi-smooth pull-backs 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 Grothendieck--Riemann--Roch type result about the compatibility of pull-backs 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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General Introduction