SoSe 18: Seminar zur Zahlentheorie "Quadratische Formen"
Lei Zhang
Comments
A quadratic form over a commutative ring is just a homogeneous polynomial of degree two in a number of variables. For example X²+Y²-Z² is a quadratic form over the integers, the real numbers or the rational numbers. Quadratic forms play very impotent roles in many branches of mathematics, especially in number theory and arithmetic algebraic geometry. The goal of this seminar is to study the quadratic forms over finite fields, local fields, the real numbers, global fields, and the integers. We are going to classify the quadratic forms over these rings. The general method is to find invariants from the quadratic forms and then classify these quadratic forms up to these invariants.
closeSuggested reading
N. Koblitz, p-adic Numbers, p-adic Analysis and Zeta-Functions, second edition, GTM 58, Springer-Verlag, 1984.
S. Lang, Algebra, GTM 211, Springer-Verlag, 2002.
J. Neukirch, Algebraic Number Theory, Springer-Verlag, 1999.
J. -P. Serre, A Course in Arithmetic, GTM 7, Springer-Verlag, 1973.
J. -P. Serre, Local Fields, GTM 67, Springer-Verlag, 1979.
13 Class schedule
Regular appointments