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\textsc{Algebra}
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\textsc{Seminar}
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\textit{Galois cohomology of function fields of p-adic curves}
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V. Suresh\par
University of Hyderabad
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\textbf{Abstract:} Let $k$ be a field and $l$ be a prime, coprime to the characteristic of $k$. Suppose
that $k$ contains the $l$-th roots of unity. Every element in the Galois cohomology
$H^n(k, \mu_l)$ is a sum of ``symbols'', thanks to a theorem of Voevodsky. It is interesting
to get bounds $N(n)$ such that every such element is a sum of at most $N(n)$ symbols,
for fields of arithmetic interest. Using recent results of Saltman, we show that if $k$
is a $p$-adic field and $p$ not equal to $l$ and $K$ is the function field of a curve over $k$,
then, $N(2) = 2$ and $N(3) = 1$.\vspace{\fill}
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Tuesday, April 24, 2007, 4:00 pm\par
Mathematics and Science Center, W303
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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