{"product_id":"descent-in-buildings-9780691166919","title":"Descent in Buildings","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eDescent 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 f\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"An impressive tour de force.\"--Bertrand Remy, Jahresbericht der DMV\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi  PART 1. MOUFANG QUADRANGLES 1\t  Chapter 1. Buildings 3  Chapter 2. Quadratic Forms 13  Chapter 3. Moufang Polygons 23  Chapter 4. Moufang Quadrangles 31  Chapter 5. Linked Tori, I 41  Chapter 6. Linked Tori, II 47  Chapter 7. Quadratic Forms over a Local Field 57  Chapter 8. Quadratic Forms of Type E6, E7 and E8 69  Chapter 9. Quadratic Forms of Type F4 79  PART 2. RESIDUES IN BRUHAT-TITS BUILDINGS 83  Chapter 10. Residues 85  Chapter 11. Unramified Quadrangles of Type E6, E7 and E8 91  Chapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8 93  Chapter 13. Ramified Quadrangles of Type E6, E7 and E8 101  Chapter 14. Quadrangles of Type E6, E7 and E8: Summary 109  Chapter 15. Totally Wild Quadratic Forms of Type E7 115  Chapter 16. Existence 119  Chapter 17. Quadrangles of Type F4 129  Chapter 18. The Other Bruhat-Tits Buildings 137  PART 3. DESCENT 141  Chapter 19. Coxeter Groups 143  Chapter 20. Tits Indices 153  Chapter 21. Parallel Residues 165  Chapter 22. Fixed Point Buildings 181  Chapter 23. Subbuildings 195  Chapter 24. Moufang Structures 205  Chapter 25. Fixed Apartments 217  Chapter 26. The Standard Metric 221  Chapter 27. Affine Fixed Point Buildings 233  PART 4. GALOIS INVOLUTIONS 241  Chapter 28. Pseudo-Split Buildings 243  Chapter 29. Linear Automorphisms 251  Chapter 30. Strictly Semi-linear Automorphisms 259  Chapter 31. Galois Involutions 271  Chapter 32. Unramified Galois Involutions 275  PART 5. EXCEPTIONAL TITS INDICES 285  Chapter 33. Residually Pseudo-Split Buildings 287  Chapter 34. Forms of Residually Pseudo-Split Buildings 297  Chapter 35. Orthogonal Buildings 303  Chapter 36. Indices for the Exceptional Bruhat-Tits Buildings 309  Bibliography 327  Index 333","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403817820503,"sku":"9780691166919","price":63.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691166919.jpg?v=1730484635","url":"https:\/\/bookcurl.com\/products\/descent-in-buildings-9780691166919","provider":"Book Curl","version":"1.0","type":"link"}