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050 4 _aQA174.2
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072 7 _aMAT
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082 0 4 _a516/.13
_223
049 _aMAIN
100 1 _aM�uhlherr, Bernhard Matthias,
_eauthor.
_964409
245 1 0 _aDescent in buildings /
_cBernhard M�uhlherr, Holger P. Petersson, Richard M. Weiss.
264 1 _aPrinceton :
_bPrinceton University Press,
_c2015.
300 _a1 online resource (xvi, 336 pages .)
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAnnals of mathematics studies ;
_v190
504 _aIncludes bibliographical references and index.
588 0 _aPrint version record.
505 0 _aCover; 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.
505 8 _aChapter 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.
505 8 _aChapter 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.
520 _aDescent 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.
546 _aIn English.
590 _aIEEE
_bIEEE Xplore Princeton University Press eBooks Library
650 0 _aBuildings (Group theory)
_964410
650 0 _aCombinatorial geometry.
_964411
650 6 _aImmeubles (Th�eorie des groupes)
_964412
650 6 _aG�eom�etrie combinatoire.
_964413
650 7 _aMATHEMATICS
_xGeometry
_xGeneral.
_2bisacsh
_97661
650 7 _aBuildings (Group theory)
_2fast
_0(OCoLC)fst00841183
_964410
650 7 _aCombinatorial geometry.
_2fast
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655 0 _aElectronic book.
_97794
655 4 _aElectronic books.
_93294
655 7 _aElectronic books.
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700 1 _aPetersson, Holger P.,
_d1939-
_eauthor.
_964414
700 1 _aWeiss, Richard M.
_q(Richard Mark),
_d1946-
_eauthor.
_964415
776 0 8 _iPrint version:
_aM�uhlherr, Bernhard Matthias.
_tDescent in buildings.
_dPrinceton : Princeton University Press, 2015
_z9780691166902
_z0691166900
_w(DLC) 2015008618
_w(OCoLC)907060235
830 0 _aAnnals of mathematics studies ;
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856 4 0 _uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452507
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