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Virtual pullbacks in K-theory

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arxiv 1608.02524 v2 pith:T67GKXGF submitted 2016-08-08 math.AG

Virtual pullbacks in K-theory

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classification math.AG
keywords theoryvirtualformulapullbacksapplicationsbivariantcertainclasses
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We consider virtual pullbacks in $K$-theory, and show that they are bivariant classes and satisfy certain functoriality. As applications to $K$-theoretic counting invariants, we include proofs of a virtual localization formula for schemes and a degeneration formula in Donaldson-Thomas theory.

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  1. Virtual Jeffrey--Kirwan localisation

    math.AG 2026-07 accept novelty 7.0

    Virtual integrals over GIT quotients X//G equal Jeffrey–Kirwan residues of virtual integrals over T-fixed loci, for perfect obstruction theories and oriented (−2)-shifted symplectic structures, in cohomology and K-theory.