to a parabolic $P \subset G$. The reduction is said to be [**canonical**]{} (or the [**Behrand reduction** ]{}) if the following conditions are satisfied:

1\) deg $E_P(P) > 0$\
2) For any parabolic subgroup scheme $Q \subset E(G)$, deg $Q \leq$ deg $E_P(P)$.\
3) For any subgroup scheme $Q \supset E_P(P)$, deg $Q <$ deg $P$.\
4)The unipotent radical bundle $E_P(P)/R_u(P)$ is semistable.\
With these conditions our definition of canonical reduction coincides with that of Behrend. $P$ is known as the [**Behrend’s parabolic**]{}. The degree of $E_P(P)$ is denoted by $deg_{HN}(E)$.

$~~$ The canonical reduction can be shown to be equivalent to the following: For any nontrivial character on $P$ which is a non-negative combination of simple roots with respect to the choice of $B$, the induced line bundle on $X$ obtained by extension of structure group has non-negative degree.

Frobenius morphism
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[\[Frobenius morphism\]]{} Let $X$ be a scheme over a algebraically closed field of char $p>0$. The $p$-th power map $\OO_X \rightarrow
\OO_X$ given by $f 
\rightarrow f^p$ gives rise to a morphism of schemes $F_X: X \rightarrow X$ called the absolute frobenius. If $k$ is a perfect field, this morphism is an isomorphism (although not a $k$-morphism 