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.
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