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

<p>Résumé :<br/>
 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.
<br/>
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.
<br/>
An application to covering radius will end the talk.