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.

中文翻译：

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刚化的躯干尾轮、超覆盖层和束状天竺葵

我们给出了更高阶的层上同调的几何解释$n\geq 1$就度数成员的躯干而言$d=n-1$在类型的超覆盖$r=n-2$，赋予了额外的基准，即所谓的刚性化。这概括了这样一个事实，即一阶上同调是扭量的同构类群，其中刚性化变得空洞，而二阶上同调可以用束 gerbe 表示，其中刚性化成为结合性约束。