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RIGIDIFIED TORSOR COCYCLES, HYPERCOVERINGS AND BUNDLE GERBES
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 112 / Issue 1 / February 2022
- Published online by Cambridge University Press:
- 07 April 2020, pp. 115-144
- Print publication:
- February 2022
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- Article
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We give a geometric interpretation of sheaf cohomology for higher degrees
$n\geq 1$ in terms of torsors on the member of degree 
$d=n-1$ in hypercoverings of type 
$r=n-2$, endowed with an additional datum, the so-called rigidification. This generalizes the fact that cohomology in degree one is the group of isomorphism classes of torsors, where the rigidification becomes vacuous, and that cohomology in degree two can be expressed in terms of bundle gerbes, where the rigidification becomes an associativity constraint.
