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# Flat cohomology for finite infinitesimal group scheme (commutativeornot) over a perfect field

Let $G$ be a finite infinitesimal group scheme (e.g.\mu_p,\alpha_p) e.g.$\mu_p,\alpha_p)$ over a perfect field $k$, how much is known about $H^1_{fppf}(k,G)$?

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Let $G$ be a finite infinitesimal group scheme (e.g.\mu_p,\alpha_p) over a perfect field $k$, how much is known about $H^1_{fppf}(k,G)$?

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# Flat cohomology for finite group scheme (commutative or not) over a perfect field

Let $G$ be a finite group scheme over a perfect field $k$, how much is known about $H^1_{fppf}(k,G)$?