Descent in Buildings:
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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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, N.J.
Princeton University Press
[2015]
|
| Series: | Annals of Mathematics Studies
number 190 |
| Subjects: | |
| Online Access: | DE-1046 DE-859 DE-860 DE-739 DE-1043 DE-858 Volltext |
| Summary: | 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 |
| Item Description: | Description based on online resource; title from PDF title page (publishers Web site, viewed September 10 2015) |
| Physical Description: | 1 Online-Ressource illustrations |
| ISBN: | 9781400874019 9780691166919 |
| DOI: | 10.1515/9781400874019 |
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| 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 | ||
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| author | Mühlherr, Bernhard M. Petersson, Holger 1939- Weiss, Richard M. 1946- |
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| dewey-ones | 516 - Geometry |
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| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400874019 |
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| spelling | Mühlherr, Bernhard M. (DE-588)1200376730 aut Descent in Buildings Bernhard Mühlherr, Holger P. Petersson, Richard M. Weiss Princeton, N.J. Princeton University Press [2015] © 2015 1 Online-Ressource illustrations txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 190 Description based on online resource; title from PDF title page (publishers Web site, viewed September 10 2015) 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 In English Algebraic topology Buildings (Group theory) Combinatorial geometry Combinatorics and Graph Theory Group theory Mathematics Mathematik Gebäude Mathematik (DE-588)4123258-6 gnd rswk-swf Gebäude Mathematik (DE-588)4123258-6 s 1\p DE-604 Petersson, Holger 1939- (DE-588)140331247 aut Weiss, Richard M. 1946- (DE-588)123955750 aut Erscheint auch als Druck-Ausgabe 978-0-691-16691-9 Annals of Mathematics Studies number 190 (DE-604)BV040389493 190 https://doi.org/10.1515/9781400874019 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mühlherr, Bernhard M. Petersson, Holger 1939- Weiss, Richard M. 1946- Descent in Buildings Annals of Mathematics Studies Algebraic topology Buildings (Group theory) Combinatorial geometry Combinatorics and Graph Theory Group theory Mathematics Mathematik Gebäude Mathematik (DE-588)4123258-6 gnd |
| subject_GND | (DE-588)4123258-6 |
| title | Descent in Buildings |
| title_auth | Descent in Buildings |
| title_exact_search | Descent in Buildings |
| title_full | Descent in Buildings Bernhard Mühlherr, Holger P. Petersson, Richard M. Weiss |
| title_fullStr | Descent in Buildings Bernhard Mühlherr, Holger P. Petersson, Richard M. Weiss |
| title_full_unstemmed | Descent in Buildings Bernhard Mühlherr, Holger P. Petersson, Richard M. Weiss |
| title_short | Descent in Buildings |
| title_sort | descent in buildings |
| topic | Algebraic topology Buildings (Group theory) Combinatorial geometry Combinatorics and Graph Theory Group theory Mathematics Mathematik Gebäude Mathematik (DE-588)4123258-6 gnd |
| topic_facet | Algebraic topology Buildings (Group theory) Combinatorial geometry Combinatorics and Graph Theory Group theory Mathematics Mathematik Gebäude Mathematik |
| url | https://doi.org/10.1515/9781400874019 |
| volume_link | (DE-604)BV040389493 |
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