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. Survey articles and the like, such as historical overviews, expository notes, and intuitive but imprecise introductions, are marked with .
- Cyclotomic Fields and Related Topics
- : 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
- Classical algebraic Iwasawa theory: historical introduction (Arizona Winter School 2018)
- Cyclotomic Fields and Zeta Values
- Galois Cohomology of Elliptic Curves
- Higher-dimensional algebraic geometry
- Stacks for Everybody
- Algebraic Geometry
- Number Theory 1–3 (Iwanami Series in Modern Mathematics)
- p-adic Numbers, p-adic Analysis, and Zeta-Functions
- Algebraic Number Theory
- Cyclotomic Fields I and II, with appendix by
- Introduction to Modular Forms
- Positivity in Algebraic Geometry
- Elementary Applied Topology
- Basic Structures of Function Field Arithmetic
- Algebraic Geometry
- Algebraic Topology
- Complex Geometry
- : Iwasawa Theory and Generalisations
- Introduction to Modern Number Theory
- Abelian Varieties
- Algebraic Number Theory
- Algebraic Geometry
- Class Field Theory
- Lectures on Étale Cohomology
- : Motives—Grothendieck's Dream (check out his other expository notes as well)
- Introduction to Algebraic K-Theory
- Algebraic Number Theory
- Cohomology of Number Fields
- Iwasawa-Theorie (unpublished notes for his course Algebraische Zahlentheorie III, WS 2014/15, Bielefeld)
- : Blow-ups in algebraic geometry
- : Derived categories of Fano fibrations
- Euler Systems
- Algebraic Geometry I, Algebraic Geometry II
- Lubin–Tate Theory
- Algebraic Groups and Class Field Theory; see Generalized Jacobians for a shorter account of the important results
- A Course in Arithmetic
- Galois Cohomology
- : Iwasawa Theory: A Climb up the Tower
- : Modular curves and cyclotomic fields (Arizona Winter School 2018)
- The Arithmetic of Elliptic Curves
- Advanced Topics in the Arithmetic of Elliptic Curves
- : On the μ-invariant in Iwasawa Theory
- : Elliptic Curves and Iwasawa's μ=0 Conjecture
- : Arithmetic of Elliptic Curves through the Ages
- Arithmetic Geometry
- Number Theory I
- Sato–Tate distributions
- Algebraic Number Theory
- Function Field Arithmetic
- The Rising Sea
- : 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
- Introduction to Cyclotomic Fields
- An Introduction to Homological Algebra
- Galois Representations
- Hida Theory
- : What is a reciprocity law? — Every student entering class field theory would do well to read the first 4 sections of this paper.
- Algebrai számelmélet