# Questions tagged [cohomology]

A branch of algebraic topology concerning the study of cocycles and coboundaries. It is in some sense a dual theory to homology theory. This tag can be further specialized by using it in conjunction with the tags group-cohomology, etale-cohomology, sheaf-cohomology, galois-cohomology, lie-algebra-cohomology, motivic-cohomology, equivariant-cohomology, ...

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### What is the smallest number $d$ such that $H^1(X,\pi^*\mathcal{O}_{\mathbb{P}_k^1}(d))$ vanishes?

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### $L_\infty$-quasi inverse for the contravariant Cartan model on principal bundles

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### Differential forms of a Lie group giving cohomology of the Lie group

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### cohomology of nilpotent matrices of fixed $m$-th power

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### De Rham cohomology of Lie groupoid

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### A cohomology associated to a (not necessarily integrable) distribution (Hilbert 16th problem and dynamical Lefschetz trace formula 2)

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### Deformations of Vertex Algebras

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### Structure of the variety of $n$-tuples of $m \times m$ matrices with zero product

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### An exact complex of tensor families

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### Conjectures of Peter Scholze about q-de Rham complex: examples

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### Homology of the universal cover

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### A cohomology associated to a vector field on a Riemannian manifold

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### Comparing cohomology using homotopy fibre

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### Cokernel of section of a general coherent sheaf

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