Alexander Sivatski: On some elements of the Brauer group of a conic

Submission: 2007, Apr 15

Let $K$ be a field of characteristic not $2$, $X$ a nonsingular projective conic over $K$, $n$ a positive integer, and $a_i\in K^*$ for $1\le i\le n$. We investigate elements of $_2 Br (X)$, which are sums of quaternion algebras $(a_i,f_i)$ for some $f_i\in K(X)^*$. An application to a construction of indecomposable division algebras of exponent $2$ is given.

2000 Mathematics Subject Classification: 16K20, 14H05

Keywords and Phrases: Quadratic form, Brauer group, Quaternion algebra, Conic

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