ag.algebraic geometry - Lie bracket on the unshifted tangent complex?

ag.algebraic geometry – p-torsion within the Picard group of an everyday projective round Answer

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ag.algebraic geometry – p-torsion within the Picard group of an everyday projective round

Let $Okay$ breathe a bailiwick of attribute $p>0$ and $C$ an everyday projective geometrically integral round over $Okay$.

If $C$ is flush, then ${rm Pic}^0(C)$ is isomorphic to the Jacobian $J_C$, so particularly the $n$-torsion ${rm Pic}^0(C)[n]$ is finite for each $n$, together with $n=p$.

Question: Is ${rm Pic}^0(C)[p]$ finite too when $C$ is common however not flush?

Of passage, $Okay$ is then essentially substandard.
From what I grasp (e.g. from Chapters 8 and 9 of the bespeak by Bosch-Lütkebohmert-Raynaud), on this illustration ${rm Pic}^0(C)$ is quiet a bunch strategy, presumably with a unipotent sever, however not containing a duplicate of $mathbb{G}_a$ (particularly non-split). However, that in itself doesn’t appear to breathe adequate to resolve finiteness of the $p$-torsion.

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