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I have the following question: let $k$ a field with $char(k)= p>0$, which we can assume to be perfect, $W(k)$ the ring of Witt vector, and $a,b$ positive integers.

Consider the ring $R=W(k)[x,y]/(x^{p^a}-1,y^{p^b}-1)$ and let


Let $T=Spec(W(k)[t])$.

Is there a way to write $X$ as a stack quotient of $U=T\coprod T$ by multiplicative of additive finite group schemes (like product or extensions of $\mu_{p^{c_i}}$ and $\alpha_{p^{d_j}}$, for some bunch of integers $c_i,d_j$)?

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