Hasse invariant of a quadratic form

The name "Hasse–Witt" comes from Helmut Hasse and Ernst Witt.The invariant may be computed for a specific symbol φ taking values in the group C2 = {±1}.[2] In the context of quadratic forms over a local field, the Hasse invariant may be defined using the Hilbert symbol, the unique symbol taking values in C2.[4] For quadratic forms over a number field, there is a Hasse invariant ±1 for every finite place.The invariants of a form over a number field are precisely the dimension, discriminant, all local Hasse invariants and the signatures coming from real embeddings.
Hasse–Witt matrixmathematicsquadratic formBrauer groupHelmut HasseErnst Wittdiagonal formquaternion algebrasStiefel–Whitney classsymbollocal fieldHilbert symboldiscriminantnumber fieldfinite placesignaturesHasse–Minkowski theoremLam, Tsit-YuenGraduate Studies in MathematicsAmerican Mathematical SocietyMilnor, J.Ergebnisse der Mathematik und ihrer GrenzgebieteSpringer-VerlagSerre, Jean-PierreGraduate Texts in Mathematics