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Degree of a finite locally free group scheme over a base scheme of characteristic p

If $f:X\rightarrow S$ is finite locally free, then formation of $f_*\mathscr{O}_X$ is compatible with arbitrary change of base on $S$. So if $X$ has constant rank $r$, i.e., $f_*\mathscr{O}_X$ is fini …
Keenan Kidwell's user avatar