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Group cohomology $H^1(G,M)$ , where $G$ is finite and $M$ is finitely generated

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#algebraic-number-theory #elliptic-curves #group-cohomology #arithmetic-geometry #galois-cohomology
71
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About the definition on cohomology of groups

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#algebraic-topology #homology-cohomology #group-cohomology #galois-cohomology
34
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Normal extension of given degree of a number field

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#number-theory #galois-theory #algebraic-number-theory #class-field-theory #galois-cohomology
104
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Galois cohomology of a finite cyclic group, 1st step

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#abstract-algebra #galois-theory #homology-cohomology #group-cohomology #galois-cohomology
77
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Why is coboundary $\sigma \to \sigma m-m$ automatically continuous?

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#abstract-algebra #general-topology #algebraic-number-theory #topological-groups #galois-cohomology
49
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Definition of coboundary of first Galois cohomology

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#abstract-algebra #number-theory #group-cohomology #galois-cohomology
45
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Image of rational characters of $p$-adic groups and Galois cohomology

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#p-adic-number-theory #algebraic-groups #galois-cohomology #reductive-groups
192
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Relation between Galois Cohomology $H^1(\text{Gal(L/K)}, L) = 0$ and $H^1(\text{Gal}(L/K), O_L)=0$

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#abstract-algebra #number-theory #algebraic-number-theory #homology-cohomology #galois-cohomology
174
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$H^1(\text{Gal}(L/K), O_L)=0$ for local fields

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#algebraic-number-theory #group-cohomology #local-field #galois-cohomology
34
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Almost purity for perfectoid fields applied on a computation of Galois cohomology.

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#number-theory #arithmetic-geometry #galois-representations #galois-cohomology
35
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Galois fixed part of modules. Why does $|(1-\sigma)A||A^G|=|A|$ hold?

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#abstract-algebra #abelian-groups #group-cohomology #fixed-points #galois-cohomology
79
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Second group cohomology of cyclic groups

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#abstract-algebra #algebraic-number-theory #group-cohomology #galois-cohomology
49
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How Galois group act on $H^1(G_L,E)$?

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#abstract-algebra #elliptic-curves #group-cohomology #arithmetic-geometry #galois-cohomology
61
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Definition of Tate-Shafarevich group up to isomorphism of elliptic curves

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#algebraic-number-theory #elliptic-curves #arithmetic-geometry #galois-cohomology
61
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The first cohomology group of automorphism group

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#group-cohomology #galois-cohomology

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