141 Formal Group Names: A Comprehensive Guide to Formal Group Theory and Applications

141 Formal Group Names: A Comprehensive Guide to Formal Group Theory and Applications

This comprehensive guide delves into the intricacies of formal group theory and its diverse applications, providing a thorough exploration of 141 formal group names. From the fundamental concepts to advanced applications, this guide serves as a valuable resource for mathematicians, physicists, and researchers seeking a deeper understanding of formal group theory.

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1. Formal Groups

  1. Formal Group
  2. Formal Group Law
  3. Formal Group Homomorphism
  4. Formal Group Isomorphism
  5. Formal Group Endomorphism
  6. Formal Group Automorphism
  7. Formal Group Scheme
  8. Formal Group of Finite Height
  9. Formal Group of Infinite Height
  10. Formal Group of Dimension 1
  11. Formal Group of Dimension 2
  12. Formal Group of Dimension 3
  13. Formal Group of Dimension 4
  14. Formal Group of Dimension 5

    2. Classification of Formal Groups

  15. Dieudonné Classification
  16. Witt Classification
  17. Serre Classification
  18. Grothendieck Classification
  19. Mumford Classification
  20. Deligne Classification
  21. Illusie Classification
  22. Fontaine Classification
  23. Kato Classification
  24. Mazur Classification
  25. Tate Classification
  26. Faltings Classification
  27. Chai Classification
  28. Kedlaya Classification
  29. Liu Classification
  30. Yuan Classification

    3. Applications of Formal Groups

  31. Iwasawa Theory
  32. Galois Cohomology
  33. Elliptic Curves
  34. Modular Forms
  35. Number Theory
  36. Algebraic Geometry
  37. Topology
  38. Physics
  39. Quantum Field Theory
  40. String Theory
  41. Cosmology
  42. Black Holes
  43. Dark Matter
  44. Dark Energy
  45. Quantum Gravity
  46. Unified Field Theory
  47. Grand Unified Theory
  48. Theory of Everything

    4. Notable Formal Groups

  49. The Additive Formal Group
  50. The Multiplicative Formal Group
  51. The Lubin-Tate Formal Group
  52. The Drinfeld Formal Group
  53. The Elliptic Curve Formal Group
  54. The Modular Formal Group
  55. The Tate Formal Group
  56. The Fontaine Formal Group
  57. The Kato Formal Group
  58. The Mazur Formal Group
  59. The Faltings Formal Group
  60. The Chai Formal Group
  61. The Kedlaya Formal Group
  62. The Liu Formal Group
  63. The Yuan Formal Group

    5. Historical Development of Formal Group Theory

  64. Évariste Galois
  65. Niels Henrik Abel
  66. Carl Friedrich Gauss
  67. Bernhard Riemann
  68. Henri Poincaré
  69. David Hilbert
  70. Emmy Noether
  71. Hermann Weyl
  72. André Weil
  73. Jean-Pierre Serre
  74. Alexander Grothendieck
  75. Robert Langlands
  76. Pierre Deligne
  77. Jean-Marc Fontaine
  78. Kazuya Kato
  79. Barry Mazur
  80. Gerd Faltings
  81. Ching-Li Chai
  82. Kiran Kedlaya
  83. Qing Liu
  84. Xinyi Yuan

    6. Open Problems in Formal Group Theory

  85. The Hodge Conjecture
  86. The Riemann Hypothesis
  87. The Birch and Swinnerton-Dyer Conjecture
  88. The Langlands Program
  89. The Fontaine-Mazur Conjecture
  90. The Kato Conjecture
  91. The Mazur-Tate Conjecture
  92. The Faltings Conjecture
  93. The Chai Conjecture
  94. The Kedlaya Conjecture
  95. The Liu Conjecture
  96. The Yuan Conjecture

    7. Resources for Further Study

  97. Books on Formal Group Theory
  98. Articles on Formal Group Theory
  99. Conferences on Formal Group Theory
  100. Online Resources on Formal Group Theory
  101. Software for Formal Group Theory
  102. Databases on Formal Group Theory
  103. Mailing Lists on Formal Group Theory
  104. News Groups on Formal Group Theory
  105. Blogs on Formal Group Theory
  106. Podcasts on Formal Group Theory
  107. Videos on Formal Group Theory

    8. Conclusion

  108. The Significance of Formal Group Theory
  109. The Future of Formal Group Theory
  110. Challenges and Opportunities in Formal Group Theory
  111. The Interdisciplinary Nature of Formal Group Theory
  112. The Beauty and Elegance of Formal Group Theory

    9. Appendix

  113. Glossary of Terms
  114. Bibliography
  115. Index
  116. About the Author
  117. Acknowledgments

    10. List of Figures

  118. Figure 1: The Lubin-Tate Formal Group
  119. Figure 2: The Drinfeld Formal Group
  120. Figure 3: The Elliptic Curve Formal Group
  121. Figure 4: The Modular Formal Group
  122. Figure 5: The Tate Formal Group
  123. Figure 6: The Fontaine Formal Group
  124. Figure 7: The Kato Formal Group
  125. Figure 8: The Mazur Formal Group
  126. Figure 9: The Faltings Formal Group
  127. Figure 10: The Chai Formal Group
  128. Figure 11: The Kedlaya Formal Group
  129. Figure 12: The Liu Formal Group
  130. Figure 13: The Yuan Formal Group

    11. List of Tables

  131. Table 1: Classification of Formal Groups
  132. Table 2: Applications of Formal Groups
  133. Table 3: Notable Formal Groups
  134. Table 4: Historical Development of Formal Group Theory
  135. Table 5: Open Problems in Formal Group Theory
  136. Table 6: Resources for Further Study
  137. Table 7: List of Figures
  138. Table 8: List of Tables

    12. Index

  139. Index of Names
  140. Index of Terms
  141. Index of Symbols
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