Frobenius Theorems in Number Theory

This lecture covers the Frobenius theorems in number theory, focusing on the relationship between ramified primes and prime divisors in number fields. It also discusses the Frobenius elements in Galois groups, ideal class groups, and norm properties. The lecture delves into the geometry of numbers, ideal class groups' finiteness, and norm multiplicative properties. Additionally, it explores the Frobenius elements' generation in Galois groups and the norm's properties with prime ideals. The lecture concludes with the properties of norm in different contexts and the proof of norm properties using the Chinese Remainder Theorem.