Witt Group - Examples

Examples

  • The Witt ring of C, and indeed any algebraically closed field or quadratically closed field, is Z/2Z.
  • The Witt ring of R is Z.
  • The Witt ring of a finite field Fq with q odd is Z/4Z if q is 3 mod 4 and isomoprphic to the group ring Z if q = 1 mod 4.
  • The Witt ring of a local field with maximal ideal of norm congruent to 1 modulo 4 is isomorphic to the group ring (Z/2Z) where V is the Klein 4-group.
  • The Witt ring of a local field with maximal ideal of norm congruent to 3 modulo 4 it is (Z/4Z) where C2 is a cyclic group of order 2.
  • The Witt ring of Q2 is of order 32 and is given by

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