These MIT lecture notes for 18.785 (Fall 2021) introduce the algebraic tools of number theory, from absolute values and Dedekind domains to ring extensions, local fields, and Galois theory. They build toward the arithmetic of number fields and global function fields.

Key Topics

• Dedekind domains
• Discrete valuation rings
• Étale algebras
• Global fields
• Frobenius elements

Author: Andrew V. Sutherland