A User's Guide to Serre's Arithmetic

G /Finite Fields/ In this chapter Serre studies the basic properties of finite fields. Of them, he gives uniqueness of finite fields of characteristic and order , gives the structure of the group , discusses solutions of polynomials over finite fields, and gives a necessary and sufficient condition for to be a field extension or the product ring . /p-adic Fields/ /Hilbert Symbol/ /Quadratic Forms Over Q p and Q / /Integral Quadratic Forms with Discriminant ±1 / /The Theorem on Arithmetic Progressions/ /Modular Forms/ References Serre - A Course in Arithmetic https://people.ucsc.edu/~weissman/Math222A/SerreAnn.pdf https://ocw.mit.edu/courses/mathematics/18-782-introduction-to-arithmetic-geometry-fall-2013/lecture-notes/ 0% Mathematics