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.