Arf's Main Results
If the field K is perfect then every nonsingular quadratic form over K is uniquely determined (up to equivalence) by its dimension and its Arf invariant. In particular this holds over the field F2. In this case U=0 and hence the Arf invariant is an element of the base field F2; it is either 0 or 1.
If the field is not perfect then the Clifford algebra is another important invariant of a quadratic form. For various fields Arf has shown that every quadratic form is completely characterized by its dimension, its Arf invariant and its Clifford algebra. Examples of such fields are function fields (or power series fields) of one variable over perfect base fields.
Read more about this topic: Arf Invariant
Famous quotes containing the words main and/or results:
“Dust rises from the main road and old Délira is stooping in front of her hut. She doesn’t look up, she softly shakes her head, her headkerchief all askew, letting out a strand of grey hair powdered, it appears, with the same dust pouring through her fingers like a rosary of misery. She repeats, “we will all die”, and she calls on the good Lord.”
—Jacques Roumain (1907–1945)
“Silence is to all creatures thus attacked the only means of salvation; it fatigues the Cossack charges of the envious, the enemy’s savage ruses; it results in a cruising and complete victory.”
—Honoré De Balzac (1799–1850)