Period Domains Over Finite and p-Adic Fields

This book is on the one hand a pedagogical introduction to the formalism of slopes of semi-stability and of related concepts in the simplest possible context. It is therefore accessible to any graduate student with a basic knowledge in algebraic geometry and algebraic groups. On the other hand the book also provides a thorough introduction to the basics of period domains as they appear in the geometric approach to local Langlands correspondences and in the recent conjectural p-adic local Langlands program. The authors provide numerous worked examples and establish many connections to topics in the general area of algebraic groups over finite and local fields. In addition the end of each section includes remarks on open questions historical context and references to the literature. Language: English