Tags: #subjects/arithmetic-geometry Refs: prism Tilting

On the importance of Tilting File:Pasted image 20211106012609.png

\({X_\mathrm{FF}}\) is also roughly a moduli of untilts, whisch allow passing between \({\mathbb{F}}_p\) and \({ {\mathbb{Q}}_p }\). A major goal is to go from characteristic zero to characteristic \(p\) (relatively easy) and then to go back to characteristic zero (relatively hard). The curve is useful because many linear algebraic objects of \(p{\hbox{-}}\)adic theory can be translated into vector bundles over \({X_\mathrm{FF}}\), and there is Grothendieck splitting type of theorem for those.