The specialization principle for p-adic kimberlites, I

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In his master thesis Lourenço proposes and proves a specialization principle for certain formal schemes. Roughly speaking, this says that a formal scheme can be recovered from its special fiber, its rigid generic fiber and the specialization map. Kimberlites were introduced by the speaker as analogues of formal schemes in Scholze's theory of v-sheaves. In forthcoming joint work with Anschütz, Lourenço and Richarz we prove a similar specialization principle for p-adic kimberlites. This result is a key step of our proof of the Scholze-Weinstein conjecture on local models of Shimura varieties.