M�uhlherr, Bernhard Matthias, <br/><br/>
Descent in buildings / 
Bernhard M�uhlherr, Holger P. Petersson, Richard M. Weiss. 
 - 1 online resource (xvi, 336 pages .) 
 - Annals of mathematics studies ;  190 .
 - Annals of mathematics studies ;  no. 190. .
<br/><br/>Includes bibliographical references and index. 
<br/><br/>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. 
<br/><br/> 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. 
<br/><br/><br/>In English. 
<br/><br/><label>ISBN: </label>9781400874019 1400874017 
<br/><br/><label>Standard No.: </label>10.1515/9781400874019  doi 
<br/><br/><label>Source: </label>815477  MIL 22573/ctt193f79s  JSTOR 9452507  IEEE 
<br/><br/><label>LCCN: </label>2015008618 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Buildings (Group theory)<br/>Combinatorial geometry.<br/>Immeubles (Th�eorie des groupes)<br/>G�eom�etrie combinatoire.<br/>MATHEMATICS--Geometry--General.<br/>Buildings (Group theory)<br/>Combinatorial geometry.
<br/><br/><label>Index Terms--Genre/Form: </label><br/>Electronic book.<br/>Electronic books.<br/>Electronic books.
<br/><br/><label>LC Class. No.: </label>QA174.2  / .M84 2015 
<br/><br/><label>Dewey Class. No.: </label>516/.13