-DISPLAYS AND RAPOPORT–ZINK SPACES

Abstract

Let $(G,\unicode[STIX]{x1D707})$ be a pair of a reductive group $G$ over the $p$-adic integers and a minuscule cocharacter $\unicode[STIX]{x1D707}$ of $G$ defined over an unramified extension. We introduce and study ‘$(G,\unicode[STIX]{x1D707})$-displays’ which generalize Zink’s Witt vector displays. We use these to define certain Rapoport–Zink formal schemes purely group theoretically, i.e. without $p$-divisible groups.