Vendredi 8 juillet 2005 à 11h en C209.
Orateur : H. F. Mattson, jr.
Titre : Without a Trace (d'après O. Moreno, F. N. Castro, et H. F. Mattson, jr.).

Résumé :
Consider a finite set of polynomials in $n$ variables over a finite field $K$ of characteristic $p$. The number $N$ of common zeros in $K^n$ of these polynomials is of interest. Ax (1964) showed that, for certain $\mu$, $p^{\mu}|N$. Katz (1971) increased the value of $\mu$ in this result. Moreno and Moreno (1995) then increased the value of $\mu$ still further in some cases.
In this talk we present a simple proof of the latter result in the case $p=2$. It is a correction to a 2003 paper of Moreno and Castro.
An application to covering radius will end the talk.