Triple

Target class: statement about Galois representations
Context triple: [Serre’s conjecture on Galois representations, instanceOf, statement about Galois representations]

• A. automorphic representation (in a broad sense)
  An automorphic representation (in a broad sense) is an irreducible unitary representation of an adelic or locally compact group that arises in the spectral decomposition of spaces of automorphic forms, encoding number-theoretic and geometric information via harmonic analysis on arithmetic quotients.
• B. result in arithmetic geometry
  A result in arithmetic geometry is a theorem or proposition that connects number-theoretic properties of solutions to polynomial equations with the geometric structure of the varieties they define over arithmetic fields.
• C. representation of a group
  A representation of a group is a homomorphism from that group into the group of linear transformations of a vector space, allowing the group’s abstract elements to be studied via concrete matrices or operators.
• D. curve over the rational numbers
  A curve over the rational numbers is an algebraic curve defined by polynomial equations with rational coefficients, considered together with its set of rational solutions and their arithmetic properties.
• E. result in representation theory chosen
  A result in representation theory is a proven statement describing how algebraic structures, such as groups or algebras, can be represented by linear transformations on vector spaces and how these representations behave or decompose.
• F. None of above.