Jean-Francois Dat is a Professor at the Université de Paris VII. Sascha Orlik is a Professor at the Universität Paderborn. Michael Rapoport is a Professor at the Universität Bonn.

'This monograph is a systematic treatise on period domains over finite and over p-adic fields. It presents the theory as it has developed over the past fifteen years … The book should serve as the basis of future research in this area.' Zentralblatt MATH

• Preface; Introduction; Part I. Period Domains for GLn Over a Finite Field: 1. Filtered vector spaces; 2. Period domains for GLn; 3. Cohomology of period domains for GLn; Part II. Period Domains for Reductive Groups over Finite Fields: 4. Interlude on the Tannakian formalism; 5. Filtrations on repk(G); 6. Period domains for reductive groups; 7. Cohomology of period domains for reductive groups; Part III. Period Domains over p-adic Fields: 8. Period domains over p-adic fields; 9. Period domains for p-adic reductive groups; 10. Cohomology of period domains over p-adic fields; Part IV. Complements: 11. Further aspects of period domains; References; Index.