Modular forms and Galois cohomology [E-Book] / Haruzo Hida.
Hida, Haruzo, (author)
Cambridge : Cambridge University Press, 2000
1 online resource (x, 343 pages)
englisch
9780511526046
9780521770361
9780521072083
Cambridge studies in advanced mathematics ; 69
Full Text
Table of Contents:
  • 1.
  • Overview of Modular Forms.
  • 1.1.
  • Hecke Characters.
  • 1.2.
  • Introduction to Modular Forms
  • 2.
  • Representations of a Group.
  • 2.1.
  • Group Representations.
  • 2.2.
  • Pseudo-representations.
  • 2.3.
  • Deformation of Group Representations
  • 3.
  • Representations of Galois Groups and Modular Forms.
  • 3.1.
  • Modular Forms on Adele Groups of GL(2).
  • 3.2.
  • Modular Galois Representations
  • 4.
  • Cohomology Theory of Galois Groups.
  • 4.1.
  • Categories and Functors.
  • 4.2.
  • Extension of Modules.
  • 4.3.
  • Group Cohomology Theory.
  • 4.4.
  • Duality in Galois Cohomology
  • 5.
  • Modular L-Values and Selmer Groups.
  • 5.1.
  • Selmer Groups.
  • 5.2.
  • Adjoint Selmer Groups.
  • 5.3.
  • Arithmetic of Modular Adjoint L-Values.
  • 5.4.
  • Control of Universal Deformation Rings.