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Descent in buildings / Bernhard M�uhlherr, Holger P. Petersson, Richard M. Weiss.

By: M�uhlherr, Bernhard Matthias [author.].
Contributor(s): Petersson, Holger P, 1939- [author.] | Weiss, Richard M. (Richard Mark), 1946- [author.].
Material type: materialTypeLabelBookSeries: Annals of mathematics studies: no. 190.Publisher: Princeton : Princeton University Press, 2015Description: 1 online resource (xvi, 336 pages .).Content type: text Media type: computer Carrier type: online resourceISBN: 9781400874019; 1400874017.Subject(s): Buildings (Group theory) | Combinatorial geometry | Immeubles (Th�eorie des groupes) | G�eom�etrie combinatoire | MATHEMATICS -- Geometry -- General | Buildings (Group theory) | Combinatorial geometryGenre/Form: Electronic book. | Electronic books. | Electronic books.Additional physical formats: Print version:: Descent in buildings.DDC classification: 516/.13 Online resources: Click here to access online
Contents:
Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. MOUFANG QUADRANGLES; Chapter 1. Buildings; Chapter 2. Quadratic Forms; Chapter 3. Moufang Polygons; Chapter 4. Moufang Quadrangles; Chapter 5. Linked Tori, I; Chapter 6. Linked Tori, II; Chapter 7. Quadratic Forms over a Local Field; Chapter 8. Quadratic Forms of Type E6, E7 and E8; Chapter 9. Quadratic Forms of Type F4; PART 2. RESIDUES IN BRUHAT-TITS BUILDINGS; Chapter 10. Residues; Chapter 11. Unramified Quadrangles of Type E6, E7 and E8; Chapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8.
Chapter 13. Ramified Quadrangles of Type E6, E7 and E8Chapter 14. Quadrangles of Type E6, E7 and E8: Summary; Chapter 15. Totally Wild Quadratic Forms of Type E7; Chapter 16. Existence; Chapter 17. Quadrangles of Type F4; Chapter 18. The Other Bruhat-Tits Buildings; PART 3. DESCENT; Chapter 19. Coxeter Groups; Chapter 20. Tits Indices; Chapter 21. Parallel Residues; Chapter 22. Fixed Point Buildings; Chapter 23. Subbuildings; Chapter 24. Moufang Structures; Chapter 25. Fixed Apartments; Chapter 26. The Standard Metric; Chapter 27. Affine Fixed Point Buildings; PART 4. GALOIS INVOLUTIONS.
Chapter 28. Pseudo-Split BuildingsChapter 29. Linear Automorphisms; Chapter 30. Strictly Semi-linear Automorphisms; Chapter 31. Galois Involutions; Chapter 32. Unramified Galois Involutions; PART 5. EXCEPTIONAL TITS INDICES; Chapter 33. Residually Pseudo-Split Buildings; Chapter 34. Forms of Residually Pseudo-Split Buildings; Chapter 35. Orthogonal Buildings; Chapter 36. Indices for the Exceptional Bruhat-Tits Buildings; Bibliography; Index.
Summary: Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups.
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Includes bibliographical references and index.

Print version record.

Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. MOUFANG QUADRANGLES; Chapter 1. Buildings; Chapter 2. Quadratic Forms; Chapter 3. Moufang Polygons; Chapter 4. Moufang Quadrangles; Chapter 5. Linked Tori, I; Chapter 6. Linked Tori, II; Chapter 7. Quadratic Forms over a Local Field; Chapter 8. Quadratic Forms of Type E6, E7 and E8; Chapter 9. Quadratic Forms of Type F4; PART 2. RESIDUES IN BRUHAT-TITS BUILDINGS; Chapter 10. Residues; Chapter 11. Unramified Quadrangles of Type E6, E7 and E8; Chapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8.

Chapter 13. Ramified Quadrangles of Type E6, E7 and E8Chapter 14. Quadrangles of Type E6, E7 and E8: Summary; Chapter 15. Totally Wild Quadratic Forms of Type E7; Chapter 16. Existence; Chapter 17. Quadrangles of Type F4; Chapter 18. The Other Bruhat-Tits Buildings; PART 3. DESCENT; Chapter 19. Coxeter Groups; Chapter 20. Tits Indices; Chapter 21. Parallel Residues; Chapter 22. Fixed Point Buildings; Chapter 23. Subbuildings; Chapter 24. Moufang Structures; Chapter 25. Fixed Apartments; Chapter 26. The Standard Metric; Chapter 27. Affine Fixed Point Buildings; PART 4. GALOIS INVOLUTIONS.

Chapter 28. Pseudo-Split BuildingsChapter 29. Linear Automorphisms; Chapter 30. Strictly Semi-linear Automorphisms; Chapter 31. Galois Involutions; Chapter 32. Unramified Galois Involutions; PART 5. EXCEPTIONAL TITS INDICES; Chapter 33. Residually Pseudo-Split Buildings; Chapter 34. Forms of Residually Pseudo-Split Buildings; Chapter 35. Orthogonal Buildings; Chapter 36. Indices for the Exceptional Bruhat-Tits Buildings; Bibliography; Index.

Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups.

In English.

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