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arXiv · 2610.27918

Rational analytic prismatization

Johannes Anschütz·Arthur-César Le Bras·Juan Esteban Rodríguez Camargo·Peter Scholze
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Abstract

We develop a general theory of analytic prismatization with $\mathbb{Q}_p$-coefficients in rigid analytic geometry over $\mathbb{Q}_p$. We prove an equivalence of perfect complexes on the perfect analytic prismatization modulo Frobenius with perfect complexes on the relative Fargues--Fontaine curve for any smooth partially proper rigid analytic variety. In particular, we explain how this equivalence conceptualizes the decompletion techniques by passing to locally analytic vectors which appear in (geometric) Sen theory

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Johannes Anschütz, Arthur-César Le Bras, Juan Esteban Rodríguez Camargo, Peter Scholze. 2026-10-20. Rational analytic prismatization. https://arxiv.org/abs/2610.27918

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