Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localizing Virtual Structure Sheaves for Almost Perfect Obstruction
  Theories   Almost perfect obstruction theories were introduced in an earlier paper by
the authors as the appropriate notion in order to define virtual structure
sheaves and $K$-theoretic invariants for many moduli stacks of interest,
including $K$-theoretic Donaldson-Thomas invariants of sheaves and complexes on
Calabi-Yau threefolds. The construction of virtual structure sheaves is based
on the $K$-theory and Gysin maps of sheaf stacks.
  In this paper, we generalize the virtual torus localization and cosection
localization formulas and their combination to the setting of almost perfect
obstruction theory. To this end, we further investigate the $K$-theory of sheaf
stacks and its functoriality properties. As applications of the localization
formulas, we establish a $K$-theoretic wall crossing formula for simple
$\mathbb{C}^\ast$-wall crossings and define $K$-theoretic invariants refining
the Jiang-Thomas virtual signed Euler characteristics.

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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: physics