Shimura reciprocity law

Target entity: Shimura reciprocity law
Context triple: [Goro Shimura, knownFor, Shimura reciprocity law]

• A. Artin reciprocity law
  The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
• B. Shimura varieties
  Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
• C. Hilbert’s twelfth problem
  Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
• D. Fontaine–Mazur conjecture
  The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
• E. Iwasawa invariants
  Iwasawa invariants are numerical parameters in algebraic number theory that measure the growth of class groups and related arithmetic objects in infinite towers of number fields studied in Iwasawa theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Shimura reciprocity law
Target entity description: The Shimura reciprocity law is a fundamental result in number theory that generalizes classical reciprocity laws by describing how values of modular functions at complex multiplication (CM) points transform under the action of Galois groups.

• A. Artin reciprocity law
  The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
• B. Shimura varieties
  Shimura varieties are higher-dimensional algebraic varieties that generalize modular curves and play a central role in the Langlands program by connecting number theory, automorphic forms, and arithmetic geometry.
• C. Hilbert’s twelfth problem
  Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
• D. Fontaine–Mazur conjecture
  The Fontaine–Mazur conjecture is a central open problem in number theory that predicts which p-adic Galois representations of number fields arise from geometry or from automorphic forms.
• E. Iwasawa invariants
  Iwasawa invariants are numerical parameters in algebraic number theory that measure the growth of class groups and related arithmetic objects in infinite towers of number fields studied in Iwasawa theory.
• F. None of above. chosen