Prismatic $F$-crystals and crystalline Galois representations
Bhargav Bhatt, Peter Scholze
Abstract
Let $K$ be a complete discretely valued field of mixed characteristic $(0,p)$ with perfect residue field. We prove that the category of prismatic $F$-crystals on $\mathcal O_K$ is equivalent to the category of lattices in crystalline $G_K$-representations.
Topics & Concepts
CrystallographyMathematicsField (mathematics)Pure mathematicsCombinatoricsGalois moduleChemistryAdvanced Algebra and GeometryAlgebraic Geometry and Number TheoryHomotopy and Cohomology in Algebraic Topology