Descent in Buildings (AM-190)
Descent in Buildings (AM-190)
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Abstract
This book begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. It then puts forward an 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” 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 The Structure of Spherical Buildings and The Structure of Affine Buildings.
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Front Matter
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Part 1 Moufang Quadrangles
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Part 2 Residues in Bruhat-Tits Buildings
- Ten Residues
- Eleven Unramified Quadrangles of Type E6, E7 and E8
- Twelve Semi-ramified Quadrangles of Type E6, E7 and E8
- Thirteen Ramified Quadrangles of Type E6, E7 and E8
- Fourteen Quadrangles of Type E6, E7 and E8: Summary
- Fifteen Totally Wild Quadratic Forms of Type E7
- Sixteen Existence
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Seventeen
Quadrangles of Type F4
Bernhard M¨uhlherr and others
- Eighteen The Other Bruhat-Tits Buildings
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Part 3 Descent
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Part 4 Galois Involutions
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Part 5 Exceptional Tits Indices
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End Matter
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