K-theory and G-theory of derived algebraic stacks

Khan, Adeel A.

doi:10.1007/s11537-021-2110-9

Cited by 4 publications

(1 citation statement)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The above vanishing result also has the following amusing corollary, which seems to be difficult to prove directly. Similar results can be proven using virtual fundamental classes in intersection theory (or graded K-theory) combined with Grothendieck-Riemann-Roch formulas; see eg [17].…”

Section: Proof Of the Algebraic Spivak's Theoremmentioning

confidence: 53%

Algebraic Spivak’s theorem and applications

Annala

2023

Geom. Topol.

View full text Add to dashboard Cite

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.14F43; 14C99, 14J99 1. Introduction 351 2. Background 357 3. Presentations of Chern classes and refined projective bundle formulas 372 4. Algebraic Spivak's theorem and applications 380 References 395

show abstract

Section: Proof Of the Algebraic Spivak's Theoremmentioning

confidence: 53%