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  1. The arithmetic properties of Shimura varieties were extensively studied by G. Shimura beginning in the early 1960s.[1]
  2. A Shimura variety whose weight is not rational is not a moduli variety, and not every Shimura variety whose weight is rational is known to be a moduli variety.[1]
  3. Roughly speaking, the goal in the study of Shimura varieties is to generalize everything that is known about modular curves to all Shimura varieties.[1]
  4. Hilbert modular surfaces and Siegel modular varieties are among the best known classes of Shimura varieties.[2]
  5. Special instances of Shimura varieties were originally introduced by Goro Shimura in the course of his generalization of the complex multiplication theory.[2]
  6. It is called the Shimura variety associated with the Shimura datum (G, X) and denoted Sh(G, X).[2]
  7. In retrospect, the name "Shimura variety" was introduced by Deligne, who proceeded to isolate the abstract features that played a role in Shimura's theory.[2]
  8. In particular, we will focus here on a sort of broad motivation for the subject—why Shimura varieties are a natural thing to study and, in particular, what they give us.[3]
  9. Third, Shimura varieties have the beautiful, but daunting, property that they have a huge range of descriptions, most of which look entirely different.[3]
  10. For this reason, it is particularly important, if one has an interest in learning about Shimura varieties, to have an upfront ‘overall perspective’.[3]
  11. Shimura varieties are objects used (conjecturally) to realize the global Langlands correspondence.[3]
  12. The theory of Shimura varieties grew out of the applications of modular functions and modular forms to number theory.[4]
  13. Roughly speaking, Shimura varieties are the varieties on which modular functions live.[4]
  14. The theory of Shimura varieties, as distinct from the theory of moduli varieties, can be said to have been born with Shimuras paper.[4]
  15. The connected Shimura varieties are the quotients of hermitian symmetric domains by the actions of certain discrete groups, which I now describe.[4]
  16. The above construction makes it clear the Shimura variety parametrizes the triples above.[5]
  17. It is thus natural to ask if we could extend the method to more general classes of Shimura varieties, relating them to certain moduli problems which behave as good as MK.[5]
  18. This leads to the PEL-type Shimura varieties, where the word "PEL" stands for polarizations, endomorphisms, and level structures.[5]
  19. AN EXAMPLE-BASED INTRODUCTION TO SHIMURA VARIETIES KAI-WEN LAN Abstract.[6]
  20. Introduction Shimura varieties are generalizations of modular curves, which have played an important role in many recent developments of number theory.[6]
  21. One of the reasons that Shimura varieties are so useful is because they carry two important kinds of symmetriesthe Hecke symmetry and the Galois symmetry.[6]
  22. However, the theory of Shimura varieties does not have a reputation of being easy to learn.[6]
  23. The original version was published as: Introduction to Shimura varieties, In Harmonic analysis, the trace formula, and Shimura varieties, 265378, Clay Math.[7]
  24. Langlands made Shimura varieties a central part of his program, both as a source of representations of Galois groups and as tests for his conjecture that all motivic L-functions are automorphic.[7]
  25. One point I should emphasize is that this is an introduction to the theory of general Shimura varieties.[7]
  26. The entire foundations of the theory of Shimura varieties need to be reworked.[7]
  27. There are two ‘local theories of Shimura varieties’ written in it.[8]
  28. Does cohomology of local shimura variety realize representations of a p-adic reductive group?[8]
  29. The term Shimura variety is usually reserved for the higher-dimensional case, in the case of one-dimensional varieties one speaks of Shimura curves.[9]
  30. In retrospect, the name Shimura variety was introduced, to recognise that these varieties form the appropriate higher-dimensional class of complex manifolds building on the idea of modular curve.[9]
  31. Abstract characterizations were introduced, to the effect that Shimura varieties are parameter spaces of certain types of Hodge structures.[9]
  32. However natural it may be to expect this, statements of this type have only been proved when X is a Shimura variety.[9]
  33. Second, to explain some of the necessary background, in particular the theory of moduli and Shimura varieties of PEL type … .[10]
  34. 1 2 SHIMURA VARIETIES OF TYPE U (1, N 1) IN CHARACTERISTIC ZERO We will sometimes let the choice of L0 vary this will correspond to looking at various connected components of the Shimura variety.[11]
  35. SHIMURA VARIETIES OF TYPE U (1, n 1) IN CHARACTERISTIC ZERO 3 Let (cid:15) B be the idempotent consisting of a 1 in the (1, 1) entry and zeros elsewhere.[11]
  36. SHIMURA VARIETIES OF TYPE U (1, n 1) IN CHARACTERISTIC ZERO 5 Now we have e1 I = . . .[11]
  37. We will leave aside important topics like compactications, bad reduction and the p-adic uniformization of Shimura varieties.[12]
  38. This is the notes of the lectures on Shimura varieties delivered by one of us in the Asia-French summer school organized at IHES in July 2006.[12]
  39. Shimura varieties of tori 5.5.[12]
  40. The relevance of Shimura varieties to automorphic forms stems from the following basic facts: ![13]
  41. It is well-known that the Shimura variety SK is geometrically disconnected.[13]
  42. Let (GSp2g; X; K) be a Shimura datum for which Kp is a hyperspecial maximal compact subgroup of GSp2g(Qp), and let SK denote the corresponding Shimura variety.[13]
  43. A classical problem due to Langlands and others which motivates much of this research is the description of the Hasse-Weil zeta function of a Shimura variety in terms of automorphic L-functions.[14]
  44. In this paper, we study the local geometry at a prime p of PEL type Shimura varieties for which there is a hyperspecial level subgroup.[15]
  45. Tate groups with additional structures and which provide a p-adic uniformization of the corresponding Shimura varieties.[15]
  46. In their work, they study the geometry of the reduction modulo p of the Shimura varieties by introducing the analogue in this context of Igusa curves, which they call Igusa varieties.[15]
  47. For general PEL type Shimura varieties, the above assumption on the dimension of the pertinent Barsotti-Tate groups does not hold.[15]
  48. We will leave aside important topics like com- pactications, bad reductions and p-adic uniformization of Shimura varieties.[16]
  49. This is the set notes for the lectures on Shimura varieties given in the Asia-French summer school organized at IHES on July 2006.[16]
  50. 2We make this precise in section 2, when we discuss Shimura varieties.[17]
  51. In this paper, we study the μ-ordinary locus of a Shimura variety with parahoric level structure.[18]
  52. Shimura varieties kind of generalize this idea.[19]
  53. This is what Shimura varieties accomplish.[19]
  54. The Shimura varieties are called Siegel modular varieties and they parametrize isogeny classes of -dimensional principally polarized abelian varieties with level structure.[19]
  55. There are many other kinds of Shimura varieties, which parametrize abelian varieties with other kinds of extra structure.[19]
  56. Tonghai will talk to us about Shimura varieties arising from orthogonal groups.[20]
  57. The quotients \H, more precisely, certain disjoint unions X of them, are the easiest examples of Shimura varieties.[21]
  58. The associated Shimura variety is then roughly \D. It is a fundamental theorem that this is in fact always an algebraic variety dened over a number eld.[21]
  59. Originally introduced by Shimura in the ‘60s in his study of the theory of complex multiplication, Shimura varieties are complex analytic varieties of great arithmetic interest.[22]
  60. We then prove a geometrical version of Serre’s Galois open image theorem for arbitrary Shimura varieties.[22]
  61. We present a general and comprehensive overview of recent developments in the theory of integral models of Shimura varieties of Hodge type.[23]
  62. The goal of the paper is to provide to non-specialists an ecient, accessible, and in depth introduction to the theory of integral models of Shimura varieties of Hodge type.[23]
  63. We begin with a motivation for the study of Shimura varieties of Hodge type.[23]
  64. They are called Shimura varieties of Hodge type (see Subsection 3.4).[23]
  65. Originally introduced by Shimura in the 60s in his study of the theory of complex multiplication, Shimura varieties are com- plex analytic varieties of great arithmetic interest.[24]
  66. You have always believed in me and supported my choices, encouraging me to nd my own path in the beautiful theory of Shimura varieties.[24]
  67. 33 2.3.2 Galois representations attached to algebraic points of Shimura varieties . . . . . . . . . . . . . . . . . . . . . .[24]

소스

  1. ↑ 1.0 1.1 1.2 Encyclopedia of Mathematics
  2. ↑ 2.0 2.1 2.2 2.3 Shimura variety
  3. ↑ 3.0 3.1 3.2 3.3 Shimura Varieties: motivation
  4. ↑ 4.0 4.1 4.2 4.3 ?w h a t
  5. ↑ 5.0 5.1 5.2 Various types of shimura variety and their moduli
  6. ↑ 6.0 6.1 6.2 6.3 An example-based introduction to shimura
  7. ↑ 7.0 7.1 7.2 7.3 Introduction to shimura varieties
  8. ↑ 8.0 8.1 A local model of a Shimura variety and a local Shimura variety
  9. ↑ 9.0 9.1 9.2 9.3 Shimura variety
  10. ↑ p-Adic Automorphic Forms on Shimura Varieties
  11. ↑ 11.0 11.1 11.2 Shimura varieties of type u (1, n − 1) in
  12. ↑ 12.0 12.1 12.2 Lectures on shimura varieties
  13. ↑ 13.0 13.1 13.2 On connected components of shimura varieties
  14. ↑ Bad Reduction of Shimura varieties
  15. ↑ 15.0 15.1 15.2 15.3 On the cohomology of certain pel type shimura
  16. ↑ 16.0 16.1 Lectures on shimura varieties
  17. ↑ Lecture notes on perfectoid shimura varieties
  18. ↑ On the μ-ordinary locus of a Shimura variety
  19. ↑ 19.0 19.1 19.2 19.3 Theories and Theorems
  20. ↑ Shimura Varieties Reading Group
  21. ↑ 21.0 21.1 Dr. fritz h¨ormann
  22. ↑ 22.0 22.1 Shimura varieties, Galois representations and motives
  23. ↑ 23.0 23.1 23.2 23.3 Geometry of shimura varieties of hodge
  24. ↑ 24.0 24.1 24.2 Shimura varieties, galois

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