08404nam 2201849 450 991082225060332120200520144314.01-4008-7401-710.1515/9781400874019(CKB)3710000000478197(SSID)ssj0001522021(PQKBManifestationID)12640759(PQKBTitleCode)TC0001522021(PQKBWorkID)11456043(PQKB)10961762(StDuBDS)EDZ0001756489(DE-B1597)460048(OCoLC)1023996695(OCoLC)1029823322(OCoLC)979624924(DE-B1597)9781400874019(Au-PeEL)EBL2028336(CaPaEBR)ebr11080905(CaONFJC)MIL815477(OCoLC)939554323(MiAaPQ)EBC2028336(EXLCZ)99371000000047819720150303d2015 uy| 0engurcnu||||||||txtccrDescent in buildings /Bernhard Mühlherr, Holger P. Petersson, and Richard M. WeissPrinceton :Princeton University Press,2015.1 online resource (353 pages) illustrationsAnnals of mathematics studies ;190Bibliographic Level Mode of Issuance: Monograph0-691-16691-9 0-691-16690-0 Includes bibliographical references and index.Frontmatter -- 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 E8 -- Chapter 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 Buildings -- Chapter 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 -- IndexDescent 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. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms.This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.Annals of mathematics studies ;190.Buildings (Group theory)Combinatorial geometryBruhat-Tits building.Clifford invariant.Coxeter diagram.Coxeter group.Coxeter system.Euclidean plane.Fundamental Theorem of Descent.Moufang building.Moufang condition.Moufang polygon.Moufang quadrangle.Moufang set.Moufang structure.Pfister form.Structure Theorem.Tits index.abelian group.absolute Coxeter diagram.absolute Coxeter system.absolute rank.affine building.algebraic group.anisotropic pseudo-quadratic space.anisotropic quadratic space.anti-isomorphism.apartment.arctic region.automorphism.bilinear form.biquaternion division algebra.building.canonical isomorphism.chamber.compatible representation.descent group.descent.discrete valuation.exceptional Moufang quadrangle.exceptional quadrangle.finite dimension.fixed point building.fixed point theory.gem.generalized quadrangle.hyperbolic plane.hyperbolic quadratic module.hyperbolic quadratic space.involutory set.isomorphism.isotropic quadratic space.length function.non-abelian group.parallel residues.polar space.projection map.proper indifferent set.proper involutory set.pseudo-quadratic space.pseudo-split building.quadratic form.quadratic module.quadratic space.quaternion division algebra.ramified quadrangle.ramified quaternion division algebra.ramified separable quadratic extension.relative Coxeter diagram.relative Coxeter group.relative Coxeter system.relative rank.residual quadratic spaces.residue.root group sequence.root.round quadratic space.scalar multiplication.semi-ramified quadrangle.separable quadratic extension.simplicial complex.special vertex.spherical building.split quadratic space.standard involution.subbuilding of split type.subbuilding.tamely ramified division algebra.thick building.thin T-building.trace map.trace.unramified quadrangle.unramified quadratic space.unramified quaternion division algebra.unramified separable quadratic extension.vector space.vertex.weak isomorphism.wild quadratic space.Buildings (Group theory)Combinatorial geometry.516/.13Mühlherr Bernhard Matthias1656234Petersson Holger P.1939-Weiss Richard M(Richard Mark),1946-MiAaPQMiAaPQMiAaPQBOOK9910822250603321Descent in buildings4008979UNINA