# Questions tagged [brauer-group]

For questions about Brauer groups; in mathematics, the Brauer group of a field $K$ is an abelian group whose elements are Morita equivalence classes of central simple algebras over $K$, with addition given by the tensor product of algebras.

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### Brauer Group for a Global Field with $l$-roots of unity $l\neq \text{char}(F)$

Let $F$ be global field that contains the $l$-roots of unity with $l$ a prime number different with the characteristic of $F$ and $\text{Br}F$ the Brauer Group of $F$. How can i proof that all ...
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### What is an example of a formal group law that does not come from an abelian variety?

I am curious to find an example of a 1-d formal group law that does not come from a splitting of the formal group law of an abelian variety. I am aware that we can craft logarithms from the formal ...
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### Realising finite abelian groups as Brauer groups of a field

Which finite abelian groups appear as Brauer groups of a field? Given a finite abelian group $G$, what are the (easiest) examples of fields with Brauer group equal to $G$?
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### On group graded algebras and Brauer groups

I was reading the paper "Algebras graded by groups" by Knus. I want to test and further my understanding of the paper by asking several questions. Since the paper is not readily available I will ...
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### On Brauer groups

The Brauer group of a braided monoidal category $\mathcal{C}$ is defined in general in this paper. Essentially it's defined as the equivalence classes of Azumaya algebras in $\mathcal{C}$ (see the ...
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### Maschke's theorem for $G$-graded algebras

I am reading the paper Algebras graded by a group of Knus. Immediately I run into problems, which I will now detail: Let $G$ be a group and $K$ a field. A $G$-graded algebra $A$ is a finite-...
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### Field with trivial Brauer group that is not of dimension $\leq 1$

In Serre's book Galois cohomology he describes an example of a field with trivial Brauer group that is not of dimension $\leq 1$, as follows: Exercise II.3.1.1. Let $k_0$ be a field of ...
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