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Classification of pseudo-reductive groups / / Brian Conrad, Gopal Prasad
| Classification of pseudo-reductive groups / / Brian Conrad, Gopal Prasad |
| Autore | Conrad Brian <1970-> |
| Pubbl/distr/stampa | Princeton, New Jersey ; ; Oxford, England : , : Princeton University Press, , 2016 |
| Descrizione fisica | 1 online resource (256 p.) |
| Disciplina | 512/.55 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Linear algebraic groups
Group theory Geometry, Algebraic |
| Soggetto non controllato |
"ient homomorphism
Cartan k-subgroup Dynkin diagram Isogeny Theorem Isomorphism Theorem Levi subgroup SeveriЂrauer variety Tits classification Tits-style classification Weil restriction algebraic geometry automorphism functor automorphism scheme automorphism canonical central extensions central "ient central extension characteristic 2. conformal isometry degenerate quadratic form double bond exotic construction field-theoretic invariant generalized exotic group generalized standard group generalized standard presentation generalized standard isomorphism class isomorphism isotropic group k-tame central extension linear isomorphism linear-algebraic invariant maximal torus minimal type non-reduced root system number theory pseudo-isogeny pseudo-reductive group pseudo-semisimple group pseudo-simple group pseudo-simple k-group pseudo-split form pseudo-split quadratic space quadrics rank-1 rank-2 rigidity property root field root system scheme-theoretic center semisimple "ient semisimple k-group structure theorem |
| ISBN | 1-4008-7402-5 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- 1. Introduction -- 2. Preliminary notions -- 3. Field-theoretic and linear-algebraic invariants -- 4. Central extensions and groups locally of minimal type -- 5. Universal smooth k-tame central extension -- 6. Automorphisms, isomorphisms, and Tits classification -- 7. Constructions with regular degenerate quadratic forms -- 8. Constructions when Φ has a double bond -- 9. Generalization of the standard construction -- A. Pseudo-isogenies -- B. Clifford constructions -- C. Pseudo-split and quasi-split forms -- D. Basic exotic groups of type F4 of relative rank 2 -- Bibliography -- Index |
| Record Nr. | UNINA-9910797511403321 |
Conrad Brian <1970->
|
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| Princeton, New Jersey ; ; Oxford, England : , : Princeton University Press, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Classification of pseudo-reductive groups / / Brian Conrad, Gopal Prasad
| Classification of pseudo-reductive groups / / Brian Conrad, Gopal Prasad |
| Autore | Conrad Brian <1970-> |
| Pubbl/distr/stampa | Princeton, New Jersey ; ; Oxford, England : , : Princeton University Press, , 2016 |
| Descrizione fisica | 1 online resource (256 p.) |
| Disciplina | 512/.55 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico |
Linear algebraic groups
Group theory Geometry, Algebraic |
| Soggetto non controllato |
"ient homomorphism
Cartan k-subgroup Dynkin diagram Isogeny Theorem Isomorphism Theorem Levi subgroup SeveriЂrauer variety Tits classification Tits-style classification Weil restriction algebraic geometry automorphism functor automorphism scheme automorphism canonical central extensions central "ient central extension characteristic 2. conformal isometry degenerate quadratic form double bond exotic construction field-theoretic invariant generalized exotic group generalized standard group generalized standard presentation generalized standard isomorphism class isomorphism isotropic group k-tame central extension linear isomorphism linear-algebraic invariant maximal torus minimal type non-reduced root system number theory pseudo-isogeny pseudo-reductive group pseudo-semisimple group pseudo-simple group pseudo-simple k-group pseudo-split form pseudo-split quadratic space quadrics rank-1 rank-2 rigidity property root field root system scheme-theoretic center semisimple "ient semisimple k-group structure theorem |
| ISBN | 1-4008-7402-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- 1. Introduction -- 2. Preliminary notions -- 3. Field-theoretic and linear-algebraic invariants -- 4. Central extensions and groups locally of minimal type -- 5. Universal smooth k-tame central extension -- 6. Automorphisms, isomorphisms, and Tits classification -- 7. Constructions with regular degenerate quadratic forms -- 8. Constructions when Φ has a double bond -- 9. Generalization of the standard construction -- A. Pseudo-isogenies -- B. Clifford constructions -- C. Pseudo-split and quasi-split forms -- D. Basic exotic groups of type F4 of relative rank 2 -- Bibliography -- Index |
| Record Nr. | UNINA-9910813208303321 |
|
Conrad Brian <1970->
|
||
| Princeton, New Jersey ; ; Oxford, England : , : Princeton University Press, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss
| Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss |
| Autore | Mühlherr Bernhard Matthias |
| Pubbl/distr/stampa | Princeton : , : Princeton University Press, , 2015 |
| Descrizione fisica | 1 online resource (353 pages) : illustrations |
| Disciplina | 516/.13 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Buildings (Group theory)
Combinatorial geometry |
| Soggetto non controllato |
Bruhat-Tits building
Clifford invariant Coxeter diagram Coxeter group Coxeter system Euclidean plane Fundamental Theorem of Descent Moufang building Moufang condition Moufang polygon Moufang quadrangle Moufang set Moufang structure Pfister form Structure Theorem Tits index abelian group absolute Coxeter diagram absolute Coxeter system absolute rank affine building algebraic group anisotropic pseudo-quadratic space anisotropic quadratic space anti-isomorphism apartment arctic region automorphism bilinear form biquaternion division algebra building canonical isomorphism chamber compatible representation descent group descent discrete valuation exceptional Moufang quadrangle exceptional quadrangle finite dimension fixed point building fixed point theory gem generalized quadrangle hyperbolic plane hyperbolic quadratic module hyperbolic quadratic space involutory set isomorphism isotropic quadratic space length function non-abelian group parallel residues polar space projection map proper indifferent set proper involutory set pseudo-quadratic space pseudo-split building quadratic form quadratic module quadratic space quaternion division algebra ramified quadrangle ramified quaternion division algebra ramified separable quadratic extension relative Coxeter diagram relative Coxeter group relative Coxeter system relative rank residual quadratic spaces residue root group sequence root round quadratic space scalar multiplication semi-ramified quadrangle separable quadratic extension simplicial complex special vertex spherical building split quadratic space standard involution subbuilding of split type subbuilding tamely ramified division algebra thick building thin T-building trace map trace unramified quadrangle unramified quadratic space unramified quaternion division algebra unramified separable quadratic extension vector space vertex weak isomorphism wild quadratic space |
| ISBN | 1-4008-7401-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- 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 E8 -- Chapter 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 Buildings -- Chapter 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 |
| Record Nr. | UNINA-9910797524903321 |
|
Mühlherr Bernhard Matthias
|
||
| Princeton : , : Princeton University Press, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss
| Descent in buildings / / Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss |
| Autore | Mühlherr Bernhard Matthias |
| Pubbl/distr/stampa | Princeton : , : Princeton University Press, , 2015 |
| Descrizione fisica | 1 online resource (353 pages) : illustrations |
| Disciplina | 516/.13 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Buildings (Group theory)
Combinatorial geometry |
| Soggetto non controllato |
Bruhat-Tits building
Clifford invariant Coxeter diagram Coxeter group Coxeter system Euclidean plane Fundamental Theorem of Descent Moufang building Moufang condition Moufang polygon Moufang quadrangle Moufang set Moufang structure Pfister form Structure Theorem Tits index abelian group absolute Coxeter diagram absolute Coxeter system absolute rank affine building algebraic group anisotropic pseudo-quadratic space anisotropic quadratic space anti-isomorphism apartment arctic region automorphism bilinear form biquaternion division algebra building canonical isomorphism chamber compatible representation descent group descent discrete valuation exceptional Moufang quadrangle exceptional quadrangle finite dimension fixed point building fixed point theory gem generalized quadrangle hyperbolic plane hyperbolic quadratic module hyperbolic quadratic space involutory set isomorphism isotropic quadratic space length function non-abelian group parallel residues polar space projection map proper indifferent set proper involutory set pseudo-quadratic space pseudo-split building quadratic form quadratic module quadratic space quaternion division algebra ramified quadrangle ramified quaternion division algebra ramified separable quadratic extension relative Coxeter diagram relative Coxeter group relative Coxeter system relative rank residual quadratic spaces residue root group sequence root round quadratic space scalar multiplication semi-ramified quadrangle separable quadratic extension simplicial complex special vertex spherical building split quadratic space standard involution subbuilding of split type subbuilding tamely ramified division algebra thick building thin T-building trace map trace unramified quadrangle unramified quadratic space unramified quaternion division algebra unramified separable quadratic extension vector space vertex weak isomorphism wild quadratic space |
| ISBN | 1-4008-7401-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Frontmatter -- 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 E8 -- Chapter 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 Buildings -- Chapter 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 |
| Record Nr. | UNINA-9910822250603321 |
|
Mühlherr Bernhard Matthias
|
||
| Princeton : , : Princeton University Press, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||