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Algebraic Spivak's theorem and applications

Toni Annala

Geometry & Topology 27 (2023) 351–396
Abstract

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.

Keywords
algebraic bordism, algebraic cobordism, derived algebraic geometry
Mathematical Subject Classification
Primary: 14F43
Secondary: 14C99, 14J99
References
Publication
Received: 1 February 2021
Revised: 8 August 2021
Accepted: 25 September 2021
Published: 1 May 2023
Proposed: Haynes R Miller
Seconded: Mark Behrens, Marc Levine
Authors
Toni Annala
Department of Mathematics
University of British Columbia
Vancouver BC
Canada

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