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I'm stucking on the proof of the Lemma 3.12 of A p-adic analogue of Borel’s theorem. Here $\mathcal A_{g,\mathrm K}$ is just a shimura variety defined over $\mathbb Z_p$, and full level $\ell$ ...

Suppose I consider a hyperelliptic curve given by an equation such as $y^2 = x^{n} + tx + 1$ or some variation on this (where $t$ is a parameter on $\mathbb P^1$ and this curve is really a surface ...

Let $\mathcal X\rightarrow C$ be a smooth projective morphism over an open subset of $\mathbb A_k^1$ ($k$ algebraically closed of characteristic $p>0$, one can suppose $C$ to be the spectrum of a ...