  In this short paper we first recall the definition and the construction of
the fundamental group scheme of a scheme $X$ in the known cases: when it is
defined over a field and when it is defined over a Dedekind scheme. It
classifies all the finite (or quasi-finite) fpqc torsors over $X$. When $X$ is
defined over a noetherian regular scheme $S$ of any dimension we do not know if
such an object can be constructed. This is why we introduce a new category,
containing the fpqc torsors, whose objects are torsors for a new topology. We
prove that this new category is cofiltered thus generating a fundamental group
scheme over $S$, said \textit{bumpy} as it may not be flat in general. We prove
that it is flat when $S$ is a Dedekind scheme, thus coinciding with the
\textit{classical} one.
