# 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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### Cohomology of BG, G non-connected Lie group, and spectral sequence relating to classifying space of connected component of the identity

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### A question about “Cohomology of Number Fields” of Neukirch

**1**

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### Rack cohomology as derived functor cohomology

**1**

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### Boundary map in Mayer-Vietoris sequence of cohomology

**4**

**1**answer

### How do I remember which power of the Lefschetz operator $L$ corresponds to the $k$th Primitive cohomology group?

**4**

**2**answers

### Low dimensional integral cohomology of $BPSO(4n)$

**3**

**2**answers

### Generalization of the Leray-Hirsch theorem

**4**

**1**answer

### Operadic cohomology in terms of infinitesimal composition

**2**

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### Looking for the exact and the precise statement of Ogus conjecture

**1**

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### Berthelot-Ogus comparison isomorphism

**3**

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### Cohomology of finite birational morphism

**2**

**1**answer

### Making coherent sheaves with nonvanishing higher Chern classes

**1**

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### Eilenberg-Steenrod cohomological theory versus Weil cohomological theory [closed]

**2**

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### The Ogus conjecture for crystalline cohomology

**10**

**1**answer

### What's the advantage of defining Lie algebra cohomology using derived functors?

**4**

**1**answer

### Higher direct image for rational singularities

**2**

**1**answer

### Computing (relative) cohomology classes on quotient (vector) space via Hodge theorem

**6**

**1**answer

### Is every additive cohomology operation stable?

**7**

**1**answer

### The (current) obstructions for a cohomological interpretation of the Riemann zeta function

**15**

**1**answer

### Multiplicative Brown representability?

**4**

**1**answer

### Compactness as a consequence of the adjunction formula for genus second homology class

**5**

**1**answer

### Using HoTT, why is twisted cohomology of BG group cohomology?

**6**

**1**answer

### Representable cohomology theories in motivic homotopy theory

**3**

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### Splitting vector bundles on $\mathbb{P}^n$

**3**

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### Obstruction to delooping

**6**

**1**answer

### Motivation for the definition of complex orientable cohomology theory

**4**

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### Relative Thom isomorphism

**6**

**2**answers

### Relation between finite dimensional representations of an affine group scheme and quasicoherent sheaves on the classifying stack

**2**

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### Killing cohomology of structure sheaf by pullback along Frobenius and finite etale covers

**5**

**2**answers

### Complement to a union of spheres in a sphere

**2**

**1**answer

### How to compute cup product of derived limits / presheaf cohomology

**5**

**1**answer

### What is the meaning of this coboundary homomorphism for group hypercohomology?

**1**

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### Road map: beyond Artin-Wedderburn theorem

**5**

**1**answer

### Cohomology of doubly pinched torus via spectral sequences

**17**

**2**answers

### A non-Abelian de Rham complex?

**5**

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### Differentials in spectral sequences and Massey products

**6**

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### Yoneda product on Ext

**2**

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### Non-trivial example of $H^2(G,M)$ where $M$ is a non-trivial G-representation

**2**

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### Definition of odd topological K-theory using circles

**19**

**3**answers

### Next steps for a Morse theory enthusiast?

**1**

**1**answer

### Cohomology with local coefficients in homotopy type theory

**1**

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### Sequence in local cohomology for multiple closed subsets

**2**

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### Rigid \'etale cohohomology of flag variety minus its rational points e.g $p$-adic Drinfeld half plane

**9**

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### An overcomplex of the Cartan model in equivariant cohomology?

**3**

**1**answer

### A cochain complex using degeneracy maps

**5**

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### triviality of homology with local coefficients

**5**

**1**answer

### Finding the right map between cohomology with local coefficients and Čech cohomology

**4**

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### Have mod $p^k$ Dyer Lashof operations been studied?

**3**

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### Evaluating the Euler class of a circle bundle on fibers

**5**

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