Algebraic Spivak's theorem and applications
Abstract
We prove an analogue of LowreySchürg's algebraic Spivak's theorem when working over a base ring $A$ that is either a field or a nice enough discrete valuation ring, and after inverting the residual characteristic exponent $e$ in the coefficients. By this result algebraic bordism groups of quasiprojective derived $A$schemes can be generated by classical cycles, leading to vanishing results for low degree $e$inverted bordism classes, as well as to the classification of quasismooth projective $A$schemes of low virtual dimension up to $e$inverted cobordism. As another application, we prove that $e$inverted bordism classes can be extended from an open subset, leading to the proof of homotopy invariance of $e$inverted bordism groups for quasiprojective derived $A$schemes.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 DOI:
 10.48550/arXiv.2101.04162
 arXiv:
 arXiv:2101.04162
 Bibcode:
 2021arXiv210104162A
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 45 pages. Submitted version