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Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
| Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz |
| Autore | Katz Nicholas M. <1943-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton ; ; Oxford, : Princeton University Press, c2012 |
| Descrizione fisica | 1 online resource (213 p.) |
| Disciplina | 515/.723 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Mellin transform
Convolutions (Mathematics) Sequences (Mathematics) |
| Soggetto non controllato |
ArtinГchreier reduced polynomial
Emanuel Kowalski EulerАoincar formula Frobenius conjugacy class Frobenius conjugacy Frobenius tori GoursatЋolchinВibet theorem Kloosterman sheaf Laurent polynomial Legendre Mellin transform Pierre Deligne Ron Evans Tannakian category Tannakian groups Zeeev Rudnick algebro-geometric autodual objects autoduality characteristic two connectedness dimensional objects duality equidistribution exponential sums fiber functor finite field Mellin transform finite field finite fields geometrical irreducibility group scheme hypergeometric sheaf interger monic polynomials isogenies lie-irreducibility lisse middle convolution middle extension sheaf monic polynomial monodromy groups noetherian connected scheme nonsplit form nontrivial additive character number theory odd characteristic odd prime orthogonal case perverse sheaves polynomials pure weight semisimple object semisimple sheaves signs split form supermorse theorem theorems |
| ISBN |
1-283-37996-1
9786613379962 1-4008-4270-0 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Introduction -- CHAPTER 1. Overview -- CHAPTER 2. Convolution of Perverse Sheaves -- CHAPTER 3. Fibre Functors -- CHAPTER 4. The Situation over a Finite Field -- CHAPTER 5. Frobenius Conjugacy Classes -- CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- CHAPTER 7. The Main Theorem -- CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- CHAPTER 9. Autodualities and Signs -- CHAPTER 10. A First Construction of Autodual Objects -- CHAPTER 11. A Second Construction of Autodual Objects -- CHAPTER 12. The Previous Construction in the Nonsplit Case -- CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- CHAPTER 17. GL(n) Examples -- CHAPTER 18. Symplectic Examples -- CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- CHAPTER 21. SL(n) Examples, for n an Odd Prime -- CHAPTER 22. SL(n) Examples with Slightly Composite n -- CHAPTER 23. Other SL(n) Examples -- CHAPTER 24. An O(2n) Example -- CHAPTER 25. G2 Examples: the Overall Strategy -- CHAPTER 26. G2 Examples: Construction in Characteristic Two -- CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- CHAPTER 28. The Situation over ℤ: Results -- CHAPTER 29. The Situation over ℤ: Questions -- CHAPTER 30. Appendix: Deligne's Fibre Functor -- Bibliography -- Index |
| Record Nr. | UNINA-9910789730903321 |
Katz Nicholas M. <1943->
|
||
| Princeton ; ; Oxford, : Princeton University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
| Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz |
| Autore | Katz Nicholas M. <1943-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton ; ; Oxford, : Princeton University Press, c2012 |
| Descrizione fisica | 1 online resource (213 p.) |
| Disciplina | 515/.723 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Mellin transform
Convolutions (Mathematics) Sequences (Mathematics) |
| Soggetto non controllato |
ArtinГchreier reduced polynomial
Emanuel Kowalski EulerАoincar formula Frobenius conjugacy class Frobenius conjugacy Frobenius tori GoursatЋolchinВibet theorem Kloosterman sheaf Laurent polynomial Legendre Mellin transform Pierre Deligne Ron Evans Tannakian category Tannakian groups Zeeev Rudnick algebro-geometric autodual objects autoduality characteristic two connectedness dimensional objects duality equidistribution exponential sums fiber functor finite field Mellin transform finite field finite fields geometrical irreducibility group scheme hypergeometric sheaf interger monic polynomials isogenies lie-irreducibility lisse middle convolution middle extension sheaf monic polynomial monodromy groups noetherian connected scheme nonsplit form nontrivial additive character number theory odd characteristic odd prime orthogonal case perverse sheaves polynomials pure weight semisimple object semisimple sheaves signs split form supermorse theorem theorems |
| ISBN |
1-283-37996-1
9786613379962 1-4008-4270-0 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Introduction -- CHAPTER 1. Overview -- CHAPTER 2. Convolution of Perverse Sheaves -- CHAPTER 3. Fibre Functors -- CHAPTER 4. The Situation over a Finite Field -- CHAPTER 5. Frobenius Conjugacy Classes -- CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- CHAPTER 7. The Main Theorem -- CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- CHAPTER 9. Autodualities and Signs -- CHAPTER 10. A First Construction of Autodual Objects -- CHAPTER 11. A Second Construction of Autodual Objects -- CHAPTER 12. The Previous Construction in the Nonsplit Case -- CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- CHAPTER 17. GL(n) Examples -- CHAPTER 18. Symplectic Examples -- CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- CHAPTER 21. SL(n) Examples, for n an Odd Prime -- CHAPTER 22. SL(n) Examples with Slightly Composite n -- CHAPTER 23. Other SL(n) Examples -- CHAPTER 24. An O(2n) Example -- CHAPTER 25. G2 Examples: the Overall Strategy -- CHAPTER 26. G2 Examples: Construction in Characteristic Two -- CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- CHAPTER 28. The Situation over ℤ: Results -- CHAPTER 29. The Situation over ℤ: Questions -- CHAPTER 30. Appendix: Deligne's Fibre Functor -- Bibliography -- Index |
| Record Nr. | UNINA-9910824873803321 |
|
Katz Nicholas M. <1943->
|
||
| Princeton ; ; Oxford, : Princeton University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Triangulated categories / / by Amnon Neeman
| Triangulated categories / / by Amnon Neeman |
| Autore | Neeman Amnon |
| Pubbl/distr/stampa | Princeton, New Jersey : , : Princeton University Press, , 2001 |
| Descrizione fisica | 1 online resource (461 p.) |
| Disciplina | 512/.55 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico | Categories (Mathematics) |
| Soggetto non controllato |
Abelian category
Abelian group Additive category Adjoint functors Adjoint Adjunction (field theory) Associative property Axiom Basis (linear algebra) Bijection Biproduct Brown's representability theorem Cardinal number Cardinality Category of abelian groups Chain complex Class (set theory) Cohomology Computation Coproduct Corollary Countable set Counterexample Derived category Derived functor Diagram (category theory) Direct limit Direct sum Discrete valuation ring Duality (mathematics) Embedding Equivalence class Equivalence of categories Exact functor Exact sequence Existence theorem Existential quantification Factorization Finitely generated abelian group Functor category Functor Grothendieck category Grothendieck's Tôhoku paper Group homomorphism Homological algebra Homotopy category of chain complexes Homotopy category Homotopy colimit Homotopy I0 Injective function Injective object Integer Isomorph Isomorphism class Jack Morava K-theory Limit (category theory) Limit of a sequence Limit ordinal Linear map Mapping cone (homological algebra) Mathematical induction Maximal ideal Module (mathematics) Monomorphism Moore space Morphism N0 Natural transformation Open set Partially ordered set Pierre Deligne Prime number Projective object Proportionality (mathematics) Quotient category Regular cardinal Representable functor Sheaf (mathematics) Special case Spectral sequence Subcategory Subobject Subsequence Subset Successor ordinal Summation Tautology (logic) Tensor product Theorem Theory Topological group Transfinite induction Transfinite Triangulated category Universal property Vector space Vladimir Voevodsky Yoneda lemma |
| ISBN |
0-691-08685-0
1-4008-3721-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- 0. Acknowledgements -- 1. Introduction -- Chapter 1. Definition and elementary properties of triangulated categories -- Chapter 2. Triangulated functors and localizations of triangulated categories -- Chapter 3. Perfection of classes -- Chapter 4. Small objects, and Thomason's localisation theorem -- Chapter 5. The category A(S) -- Chapter 6. The category Εx (Sop, Ab) -- Chapter 7. Homological properties of Εx(Sop,Αb) -- Chapter 8. Brown representability -- Chapter 9. Bousfield localisation -- Appendix A. Abelian categories -- Appendix B. Homological functors into [AB5α] categories -- Appendix C. Counterexamples concerning the abelian category A(Τ) -- Appendix D. Where Τ is the homotopy category of spectra -- Appendix E. Examples of non-perfectly-generated categories -- Bibliography -- Index |
| Record Nr. | UNINA-9910791958903321 |
|
Neeman Amnon
|
||
| Princeton, New Jersey : , : Princeton University Press, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Triangulated categories / / by Amnon Neeman
| Triangulated categories / / by Amnon Neeman |
| Autore | Neeman Amnon |
| Pubbl/distr/stampa | Princeton, New Jersey : , : Princeton University Press, , 2001 |
| Descrizione fisica | 1 online resource (461 p.) |
| Disciplina | 512/.55 |
| Collana | Annals of Mathematics Studies |
| Soggetto topico | Categories (Mathematics) |
| Soggetto non controllato |
Abelian category
Abelian group Additive category Adjoint functors Adjoint Adjunction (field theory) Associative property Axiom Basis (linear algebra) Bijection Biproduct Brown's representability theorem Cardinal number Cardinality Category of abelian groups Chain complex Class (set theory) Cohomology Computation Coproduct Corollary Countable set Counterexample Derived category Derived functor Diagram (category theory) Direct limit Direct sum Discrete valuation ring Duality (mathematics) Embedding Equivalence class Equivalence of categories Exact functor Exact sequence Existence theorem Existential quantification Factorization Finitely generated abelian group Functor category Functor Grothendieck category Grothendieck's Tôhoku paper Group homomorphism Homological algebra Homotopy category of chain complexes Homotopy category Homotopy colimit Homotopy I0 Injective function Injective object Integer Isomorph Isomorphism class Jack Morava K-theory Limit (category theory) Limit of a sequence Limit ordinal Linear map Mapping cone (homological algebra) Mathematical induction Maximal ideal Module (mathematics) Monomorphism Moore space Morphism N0 Natural transformation Open set Partially ordered set Pierre Deligne Prime number Projective object Proportionality (mathematics) Quotient category Regular cardinal Representable functor Sheaf (mathematics) Special case Spectral sequence Subcategory Subobject Subsequence Subset Successor ordinal Summation Tautology (logic) Tensor product Theorem Theory Topological group Transfinite induction Transfinite Triangulated category Universal property Vector space Vladimir Voevodsky Yoneda lemma |
| ISBN |
0-691-08685-0
1-4008-3721-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- 0. Acknowledgements -- 1. Introduction -- Chapter 1. Definition and elementary properties of triangulated categories -- Chapter 2. Triangulated functors and localizations of triangulated categories -- Chapter 3. Perfection of classes -- Chapter 4. Small objects, and Thomason's localisation theorem -- Chapter 5. The category A(S) -- Chapter 6. The category Εx (Sop, Ab) -- Chapter 7. Homological properties of Εx(Sop,Αb) -- Chapter 8. Brown representability -- Chapter 9. Bousfield localisation -- Appendix A. Abelian categories -- Appendix B. Homological functors into [AB5α] categories -- Appendix C. Counterexamples concerning the abelian category A(Τ) -- Appendix D. Where Τ is the homotopy category of spectra -- Appendix E. Examples of non-perfectly-generated categories -- Bibliography -- Index |
| Record Nr. | UNINA-9910821730503321 |
|
Neeman Amnon
|
||
| Princeton, New Jersey : , : Princeton University Press, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||