| Week | Date | Topic | Relevant Katok Reading | Further Resources | | --- | --- | --- | --- | --- | | ✅ 0 | 1/23 | Organizational Meet + Greet | | | | ✅ 1 | 1/28 | Introducing P-adics Part I | 1.1, 1.2, 1.3 | Equivalence of Absolute Values [K. Conrad] Equivalence of Norms [K. Conrad] Metric Spaces [K. Conrad] The P-adic Expanson of Rational Numbers [K. Conrad] | | ✅ 2 | 2/4 | Introducing P-Adics Part II | 1.4 | Modular Arithmetic [K. Conrad] | | ✅ 3 | 2/11 | The Arithmetic and Algebra of Q_p and Z_p | 1.5, 1.6, 1.8 | Standard Definitions for Rings [K. Conrad] Modular Arithmetic [K. Conrad] The Local-Global Principle [K. Conrad] | | ✅ 4 | 2/18 | Hensel’s Theorem I | 1.7, 1.9, 1.10 (optionally) | Modular Arithmetic [K. Conrad] Hensel’s Lemma [K. Conrad]
Ostrowski’s Theorem for Number Fields [K. Conrad] Compare to Ostrowski’s Theorem for Q [K. Conrad[ | | ✅ 5 | 2/25 | Hensel’s Theorem II | 1.7, 1.9, 1.10 (optionally) | Modular Arithmetic [K. Conrad] Hensel’s Lemma [K. Conrad]
Ostrowski’s Theorem for Number Fields [K. Conrad] Compare to Ostrowski’s Theorem for Q [K. Conrad[ | | | | MIDTERMS | | | | | | SPRING BREAK | | | | ✅ 6 | 3/18 | Introducing P-adic Power Series | 3.1, 3.2 | Infinite Series in P-adic Fields [K. Conrad] | | ✅ 7 | 3/25 | P-Adic Geo Part I | N/A | Talk Notes distributed via mailing list | | ✅ 8 | 4/1 | P-Adic Geo Part II | N/A | Talk Notes distributed via mailing list | | ✅ 9 | 4/8 | A P-Adic Problem Session | N/A | Problem Set 1 [PAWS 2024] | | 10 | 4/15 | Continuity and Locally Constant Functions | 4.1, 4.2, 4.4 | | | 11 | 4/22 | TBD | TBD | TBD | | 12 | 4/29 | TBD | TBD | TBD | | | | FINALS | | Some Further Directions with P-adics:

History of Class Field Theory [K. Conrad] Representations of p-adic Groups [J. Fintzen] Adic Spaces [S. Morel] Several Approaches to Non-archimedian Geometry [B. Conrad] |