Descent in Buildings (AM-190) /

Descent in Buildings (AM-190) / / Richard M. Weiss, Holger P. Petersson, Bernhard Mühlherr.

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 nece...

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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Mühlherr, Bernhard,
Petersson, Holger P.,
Weiss, Richard M.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2015]
©2016
Year of Publication:2015
Language:English
Series:Annals of Mathematics Studies ; 190
Online Access:
Physical Description:1 online resource (352 p.) :; 22 line illus. 8 tables.
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019 |a (OCoLC)1023996695 
019 |a (OCoLC)1029823322 
020 |a 9781400874019 
024 7 |a 10.1515/9781400874019  |2 doi 
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100 1 |a Mühlherr, Bernhard,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Descent in Buildings (AM-190) /  |c Richard M. Weiss, Holger P. Petersson, Bernhard Mühlherr. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2015] 
264 4 |c ©2016 
300 |a 1 online resource (352 p.) :  |b 22 line illus. 8 tables. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 0 |a Annals of Mathematics Studies ;  |v 190 
505 0 0 |t Frontmatter --   |t Contents --   |t Preface --   |t PART 1. Moufang Quadrangles --   |t Chapter 1. Buildings --   |t Chapter 2. Quadratic Forms --   |t Chapter 3. Moufang Polygons --   |t Chapter 4. Moufang Quadrangles --   |t Chapter 5. Linked Tori, I --   |t Chapter 6. Linked Tori, II --   |t Chapter 7. Quadratic Forms over a Local Field --   |t Chapter 8. Quadratic Forms of Type E6, E7 and E8 --   |t Chapter 9. Quadratic Forms of Type F4 --   |t PART 2. Residues in Bruhat-Tits Buildings --   |t Chapter 10. Residues --   |t Chapter 11. Unramified Quadrangles of Type E6, E7 and E8 --   |t Chapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8 --   |t Chapter 13. Ramified Quadrangles of Type E6, E7 and E8 --   |t Chapter 14. Quadrangles of Type E6, E7 and E8: Summary --   |t Chapter 15. Totally Wild Quadratic Forms of Type E7 --   |t Chapter 16. Existence --   |t Chapter 17. Quadrangles of Type F4 --   |t Chapter 18. The Other Bruhat-Tits Buildings --   |t PART 3. Descent --   |t Chapter 19. Coxeter Groups --   |t Chapter 20. Tits Indices --   |t Chapter 21. Parallel Residues --   |t Chapter 22. Fixed Point Buildings --   |t Chapter 23. Subbuildings --   |t Chapter 24. Moufang Structures --   |t Chapter 25. Fixed Apartments --   |t Chapter 26. The Standard Metric --   |t Chapter 27. Affine Fixed Point Buildings --   |t PART 4. Galois Involutions --   |t Chapter 28. Pseudo-Split Buildings --   |t Chapter 29. Linear Automorphisms --   |t Chapter 30. Strictly Semi-linear Automorphisms --   |t Chapter 31. Galois Involutions --   |t Chapter 32. Unramified Galois Involutions --   |t PART 5. Exceptional Tits Indices --   |t Chapter 33. Residually Pseudo-Split Buildings --   |t Chapter 34. Forms of Residually Pseudo-Split Buildings --   |t Chapter 35. Orthogonal Buildings --   |t Chapter 36. Indices for the Exceptional Bruhat-Tits Buildings --   |t Bibliography --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Buildings (Group theory). 
650 0 |a Combinatorial geometry. 
650 7 |a MATHEMATICS / Group Theory.  |2 bisacsh 
653 |a Bruhat-Tits building. 
653 |a Clifford invariant. 
653 |a Coxeter diagram. 
653 |a Coxeter group. 
653 |a Coxeter system. 
653 |a Euclidean plane. 
653 |a Fundamental Theorem of Descent. 
653 |a Moufang building. 
653 |a Moufang condition. 
653 |a Moufang polygon. 
653 |a Moufang quadrangle. 
653 |a Moufang set. 
653 |a Moufang structure. 
653 |a Pfister form. 
653 |a Structure Theorem. 
653 |a Tits index. 
653 |a abelian group. 
653 |a absolute Coxeter diagram. 
653 |a absolute Coxeter system. 
653 |a absolute rank. 
653 |a affine building. 
653 |a algebraic group. 
653 |a anisotropic pseudo-quadratic space. 
653 |a anisotropic quadratic space. 
653 |a anti-isomorphism. 
653 |a apartment. 
653 |a arctic region. 
653 |a automorphism. 
653 |a bilinear form. 
653 |a biquaternion division algebra. 
653 |a building. 
653 |a canonical isomorphism. 
653 |a chamber. 
653 |a compatible representation. 
653 |a descent group. 
653 |a descent. 
653 |a discrete valuation. 
653 |a exceptional Moufang quadrangle. 
653 |a exceptional quadrangle. 
653 |a finite dimension. 
653 |a fixed point building. 
653 |a fixed point theory. 
653 |a gem. 
653 |a generalized quadrangle. 
653 |a hyperbolic plane. 
653 |a hyperbolic quadratic module. 
653 |a hyperbolic quadratic space. 
653 |a involutory set. 
653 |a isomorphism. 
653 |a isotropic quadratic space. 
653 |a length function. 
653 |a non-abelian group. 
653 |a parallel residues. 
653 |a polar space. 
653 |a projection map. 
653 |a proper indifferent set. 
653 |a proper involutory set. 
653 |a pseudo-quadratic space. 
653 |a pseudo-split building. 
653 |a quadratic form. 
653 |a quadratic module. 
653 |a quadratic space. 
653 |a quaternion division algebra. 
653 |a ramified quadrangle. 
653 |a ramified quaternion division algebra. 
653 |a ramified separable quadratic extension. 
653 |a relative Coxeter diagram. 
653 |a relative Coxeter group. 
653 |a relative Coxeter system. 
653 |a relative rank. 
653 |a residual quadratic spaces. 
653 |a residue. 
653 |a root group sequence. 
653 |a root. 
653 |a round quadratic space. 
653 |a scalar multiplication. 
653 |a semi-ramified quadrangle. 
653 |a separable quadratic extension. 
653 |a simplicial complex. 
653 |a special vertex. 
653 |a spherical building. 
653 |a split quadratic space. 
653 |a standard involution. 
653 |a subbuilding of split type. 
653 |a subbuilding. 
653 |a tamely ramified division algebra. 
653 |a thick building. 
653 |a thin T-building. 
653 |a trace map. 
653 |a trace. 
653 |a unramified quadrangle. 
653 |a unramified quadratic space. 
653 |a unramified quaternion division algebra. 
653 |a unramified separable quadratic extension. 
653 |a vector space. 
653 |a vertex. 
653 |a weak isomorphism. 
653 |a wild quadratic space. 
700 1 |a Petersson, Holger P.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Weiss, Richard M.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Annals of Mathematics eBook-Package 1940-2020  |z 9783110494914  |o ZDB-23-PMB 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press Complete eBook-Package 2014-2015  |z 9783110665925 
776 0 |c print  |z 9780691166902 
856 4 0 |u https://doi.org/10.1515/9781400874019 
856 4 0 |u https://www.degruyter.com/isbn/9781400874019 
856 4 2 |3 Cover  |u https://www.degruyter.com/document/cover/isbn/9781400874019/original 
912 |a 978-3-11-066592-5 Princeton University Press Complete eBook-Package 2014-2015  |c 2014  |d 2015 
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