Things I (have) read
This is a list of mathematical writings (mostly books, lecture notes, survey articles, or seminar notes) with which I had contact in the past. The list is by no means complete, and it is intended primarily for my own use. At some point, this list should be organised by topic. Mathematics is not a disjoint union of closed subsets (i.e. it is connected), hence the topical organisation below is necessarily somewhat arbitrary. Survey articles and the like, such as historical overviews, expository notes, and intuitive but imprecise introductions, are marked with .
Algebraic Number Theory
- Algebraic Number Theory
- Number Theory 1–3 (Iwanami Series in Modern Mathematics)
- Algebraic Number Theory
- Algebraic Number Theory
- Maximal Orders
- Number Theory I
- Algebraic Number Theory
- Algebrai számelmélet
Class Field Theory
- Class Field Theory
- Lubin–Tate Theory
- : What is a reciprocity law? — Every student entering class field theory would do well to read the first 4 sections of this paper.
Cyclotomic Fields & Iwasawa Theory
- Cyclotomic Fields and Related Topics
- Classical algebraic Iwasawa theory: historical introduction (Arizona Winter School 2018)
- Cyclotomic Fields and Zeta Values
- : Iwasawa Theory and Generalisations
- Cyclotomic Fields I and II, with appendix by
- About Main Conjectures — not a thorough explanation, but illuminating
- : Iwasawa Theory: A Climb up the Tower
- Introduction to Cyclotomic Fields
Function Field Arithmetic
- Basic Structures of Function Field Arithmetic
- Function Field Arithmetic
Modular forms
- Introduction to Modular Forms
- : Modular curves and cyclotomic fields (Arizona Winter School 2018)
Arithmetic Geometry (incl. Elliptic Curves)
- Abelian Varieties
- Euler Systems
- The Arithmetic of Elliptic Curves
- Advanced Topics in the Arithmetic of Elliptic Curves
- Arithmetic Geometry
- Hida Theory
Miscellaneous Algebra
- Methods of Representation Theory I–II
- An Introduction to Homological Algebra
Algebraic Geometry
- Algebraic Geometry
- Positivity in Algebraic Geometry
- Algebraic Geometry
- : Blow-ups in algebraic geometry
- : Derived categories of Fano fibrations
- Algebraic Geometry I, Algebraic Geometry II
- The Rising Sea
Complex Geometry
- Complex Geometry
Algebraic Topology
- Elementary Applied Topology
- Algebraic Topology
Miscellany
Unsorted
- : p-adic L-functions and Euler systems: a tale in two trilogies
- : Regulators, L-functions and rational points — survey of Dirichlet L-functions and L-functions of elliptic curves as well as their p-adic counterparts, indicating analogies
- : Report on the Birch and Swinnerton-Dyer Conjecture — overview of Mordell-Weil and BSD, surveys recent results on BSD
- Galois Cohomology of Elliptic Curves
- Higher-dimensional algebraic geometry
- Stacks for Everybody
- p-adic Numbers, p-adic Analysis, and Zeta-Functions
- Introduction to Modern Number Theory
- Lectures on Étale Cohomology
- : Motives—Grothendieck's Dream (check out his other expository notes as well)
- Introduction to Algebraic K-Theory
- Cohomology of Number Fields
- Algebraic Groups and Class Field Theory; see Generalized Jacobians for a shorter account of the important results
- A Course in Arithmetic
- Galois Cohomology
- : On the μ-invariant in Iwasawa Theory
- : Elliptic Curves and Iwasawa's μ=0 Conjecture
- : Arithmetic of Elliptic Curves through the Ages
- Sato–Tate distributions
- : Können ζ-Funktionen Diophantische Gleichungen lösen? (Eine Einführung zur (nicht-kommutativen) Iwasawa-Theorie)
- : From classical to non-commutative Iwasawa theory – an introduction to the GL2 main conjecture
- : From the Birch and Swinnerton Dyer Conjecture over the Equivariant Tamagawa Number Conjecture to non-commutative Iwasawa theory
- Galois Representations