Algebraic Spivak’s theorem and applications

Annala, Toni¹

¹ Department of Mathematics, University of British Columbia, Vancouver BC, Canada

Geometry & topology, Tome 27 (2023) no. 1, pp. 351-396.

Résumé

We prove an analogue of Lowrey and Schürg’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.

Détail

DOI : 10.2140/gt.2023.27.351

Keywords: algebraic bordism, algebraic cobordism, derived algebraic geometry

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