BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Polynomials over central division algebras (joint with Shira Gilat) Matzri, Eli


Let $F$ be a field which is prime to $p$ closed. We show that any twisted polynomial in $D[y,\sigma]$ of degree at most $p-1$ ($K/F$ a cyclic Galois extension of degree $p$) splits into linear factors. As an application we show that a standard Kummer space is a degree $p$ symbol algebra $D=(a,b)_{p,F}$ generates the multiplicative group $D^{\times}$. We also show that $GL_p(F)$ is also generated by any standard Kummer space.

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