# Learning Resources: Number Theory #MOC/resources ### Class Field Theory Advice: - Look at [global class field theory](global%20class%20field%20theory) first, see book of Janusz. - Washington's Cyclotomic Fields. - Harari's book (?) - Artin and Tate's notes - Interesting topics: Resources - [Brief summary of statements of CFT](https://math.mit.edu/~poonen/papers/cft.pdf) #resources/summaries - [Blogpost introducing CFT "Local class field theory: a discussion"](https://ayoucis.wordpress.com/2015/09/01/local-class-field-theory-a-discussion/) - [Milne's Notes](https://www.jmilne.org/math/CourseNotes/CFT.pdf) - [Cassels-Frohlich](https://www.math.arizona.edu/~cais/scans/Cassels-Frohlich-Algebraic_Number_Theory.pdf) - [Cox: Primes of the form...](http://www.math.toronto.edu/~ila/Cox-Primes_of_the_form_x2+ny2.pdf) - [OCW Lecture Notes](https://ocw.mit.edu/courses/mathematics/18-786-number-theory-ii-class-field-theory-spring-2016/lecture-notes/) [Seminar on Iwasawa theory](https://math.mit.edu/nt/old/stage_f17.html) Galois cohomology: ### Algebraic Number Theory See [Learning Algebraic Number Theory](Learning%20Algebraic%20Number%20Theory) ### Modular Forms - [AWS 2021](https://www.math.arizona.edu/~swc/) ## Arithmetic Geometry - [https://math.mit.edu/nt/index_stage](https://math.mit.edu/nt/index_stage) - [Seminar talks on the Weil conjectures](https://math.mit.edu/nt/old/stage_f20.html) - [Seminar on unlikely intersections and o-minimality](https://math.mit.edu/nt/old/stage_s19.html) ### Abelian Varieties - [http://www.math.columbia.edu/~chaoli/docs/AbelianVarieties.html](http://www.math.columbia.edu/~chaoli/docs/AbelianVarieties.html) - See Haiyang's notes: [moduli stack of abelian varieties > ^7cc3c7](moduli%20stack%20of%20abelian%20varieties#^7cc3c7) ### Rational Points - ## Langlands - See [The Langlands Program](The%20Langlands%20Program) - [attachments/Geometric Langlands, Perfectoid Spaces, Fargues-Fontaine Overview.pdf](attachments/Geometric%20Langlands,%20Perfectoid%20Spaces,%20Fargues-Fontaine%20Overview.pdf) - [attachments/Friedberg - 2018 - WHAT IS ...the Langlands Program.pdf](attachments/Friedberg%20-%202018%20-%20WHAT%20IS%20...the%20Langlands%20Program.pdf) - [MSRI Summer School on automorphic forms and the Langlands program](https://www.msri.org/summer_schools/792) - [Projects/2022 AWS/Automorphic Forms and Langlands Kevin Buzzard Notes](Projects/2022%20AWS/Automorphic%20Forms%20and%20Langlands%20Kevin%20Buzzard%20Notes.md) # Misc ## Some Courses at Stanford, 2014-2019 --- Course Title Lecturer 249A (2018) [Automorphy Lifting](https://www.mit.edu/~fengt/249A_2018.pdf) (in progress) Richard Taylor 249C (2017) [Geometric Quantization and Representation Theory](https://www.mit.edu/~fengt/249C_2017.pdf) (in progress) Akshay Venkatesh 249B (2017) Alterations. (Due to a broken hand, this was picked up by [Aaron Landesman](http://web.stanford.edu/~aaronlan/assets/alterations-notes.pdf).) Brian Conrad 245C (2016) [Geometry of Numbers](https://www.mit.edu/~fengt/245C_2016.pdf) Akshay Venkatesh [249B (2016)](http://math.stanford.edu/~conrad/249BW16Page/) [Reductive Groups over Fields](https://www.mit.edu/~fengt/249B_2016.pdf) Brian Conrad [245B (2016)](http://math.stanford.edu/~jli/Topics%20in%20AG.html) [Enumerating Curves in Calabi-Yau Threefolds](https://www.mit.edu/~fengt/245B_2016.pdf) (under revision) Jun Li 258 (2016) [Higgs Bundles and Non-Abelian Hodge Theory](https://www.mit.edu/~fengt/258.pdf) (under revision) Rafe Mazzeo 263C (2015) [The Analytic Class Number Formula and L-functions](https://www.mit.edu/~fengt/263C.pdf) (Under revision) Akshay Venkatesh [245C (2015)](http://web.stanford.edu/~zli2/math245C/) [Automorphic Forms on Shimura Varieties](https://www.mit.edu/~fengt/245C.pdf) (Under revision) Zhiyuan Li [249C (2015)](http://math.stanford.edu/~conrad/249CS15Page/) [Abelian Varieties](https://www.mit.edu/~fengt/249C.pdf) (Under revision) Brian Conrad [282C (2015)](http://web.stanford.edu/~danbe/teaching/IndexThm.html) [Fiber Bundles and Cobordism](https://www.mit.edu/~fengt/282C.pdf) (Under revision) Dan Berwick-Evans [245B (2015)](http://math.stanford.edu/~vakil/15-245/) [Equivariant Algebraic Geometry](https://www.mit.edu/~fengt/EquivAG.pdf) Ravi Vakil [263B (2015)](http://sporadic.stanford.edu/modrep) [Modular Representation Theory](https://www.mit.edu/~fengt/mod_rep_theory.pdf) Dan Bump 249B (2015) [The Langlands Correspondence for Global Function Fields](https://www.mit.edu/~fengt/FFL.pdf) Zhiwei Yun [248 (2014)](http://math.stanford.edu/~mmirzakh/Math248.html) [Introduction to Ergodic Theory](https://www.mit.edu/~fengt/ergodic_theory.pdf) Maryam Mirzakhani