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Abstract The primary goal of this paper is to identify syntomic complexes with the p -adic étale Tate twists of Geisser–Sato–Schneider on regular p -torsion-free schemes. Our methods apply naturally to a broader class of schemes that we call ‘ F -smooth’. The F -smoothness of regular schemes leads to new results on the absolute prismatic cohomology of regular schemes.more » « less
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Abstract We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global $$F$$ F -regularity to mixed characteristic and identify certain stable sections of adjoint line bundles. Finally, by passing to graded rings, we generalize a special case of Fujita’s conjecture to mixed characteristic.more » « less
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We prove a generic smoothness result in rigid analytic geometry over a characteristic zero non-archimedean field. The proof relies on a novel notion of generic points in rigid analytic geometry which are well adapted to ‘spreading out’ arguments, in analogy with the use of generic points in scheme theory. As an application, we develop a six-functor formalism for Zariski-constructible étale sheaves on characteristic zero rigid spaces. Among other things, this implies that characteristic zero rigid spaces support a well-behaved theory of perverse sheaves.more » « less
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