Alexander Sivatski:: On the Faddeev index of an algebra over the function field of a curve

Submission: 2007, May 5

We give an upper bound for the Faddeev index of a central simple algebra of prime exponent $p$ over the rational function field in the case where the ramification sequence of the algebra consists of rational points. This bound depends only on the number of ramification points and in many cases turns out to be strict. Let $k$ be a field containing a primitive $p$-th root of unity, $X$ a smooth complete curve over $k$. We show that there exist algebras of exponent $p$ over $k(X)$ with arbitrarily large Faddeev index, provided that there are algebras of exponent $p$ and arbitrarily large index over $k$.

2000 Mathematics Subject Classification: 13C12, 13F20

Keywords and Phrases: Cyclic algebra, ramification sequence, etale cohomology group, residue map

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