Lecture Notes

Abelian Varieties

• Lecture notes on Abelian Varieties by J.S. Milne (dvi, ps, pdf; E), Bas Edixhoven (ps.gz, FR), Wolfgang Ruppert (ps.gz, D), Polishchuk
• Lecture notes on Jacobian Varieties by Bas Edixhoven (ps.gz, FR),
• Explicit approaches to modular Abelian varieties; thesis by W. Stein (tex, dvi, ps; E)

Algebra

• Lecture Notes by Bas Edixhoven (tex, ps, ps.gz, FR), Paul Garrett (ps, E; also as pdf ), B. Külshammer (dvi, D), Lee Lady (dvi, ps; E), Schwaenzl (ps.gz, D), Spindler (ps.gz, D)
• Lecture notes by Karl Mathiak: Introduction (ps, D), Algebra (ps, D), valuations (ps, D), Krull valuations (ps, D), real valuations (ps, D), Algebra for computer scientists (ps, D), computer algebra (pdf, D).
• Lecture Notes on rings by B. Külshammer (dvi, D)

Algebraic Geometry

• Lecture notes on Algebraic Geometry by J.S. Milne (dvi, ps, pdf; E), Antoine Chambert-Loir (ps.gz, FR, also as pdf), M. Flach G. Harder (dvi, D; also as ps); parts of this huge file will appear as a book: here are the ps and pdf files.
• Introduction to Algebraic Geometry by Ravi Vakil (dvi, ps, pdf; E), Igor Dolgachev (tex, ps; E), Oliver Debarre (ps, FR), Hartshorne (dvi, ps.gz; E; texed by W. Stein), Wolfgang Ruppert (ps.gz, D), who also has a second course (ps.gz, D), Alexei N. Skorobogatov (dvi, E). Spindler (ps.gz, D), Kevin Coombes (dvi, E)
• Introductional surveys for Algebraic Geometry by David Madore (dvi, FR), also as ps.gz (FR)
• Lecture Notes on Algebraic Curves by Hendrik Lenstra (dvi, ps; E)
• Introduction to Schemes by Wolfgang Ruppert (ps.gz, D)
• Seminar on Algebraic Geometry by Michael Harrison
• Theorem of Belyi by D.Madore, J.Marot (ps.gz, FR)

Algebraic Groups

Notes on Arithmetic Groups by Dave Witte (pdf; E)

Algebraic K-Theory

• The book in progress by Charles Weibel (dvi; E)
• Matsumoto's calculations for K₂ by G.Laget, O.Teulié (dvi.gz, FR)
• Survey of the work of Soulé and Kurihara on Vandiver's Conjecture by Eknath Ghate (dvi, E)
• Lecture notes on K_n of number fields by Joel Riou
• Kolster's survey of K-theory and arithmetic (dvi, ps; E)

Algebraic Number Theory

• Lecture notes on Algebraic Number Theory by J.S. Milne (dvi, ps, pdf; E), L. Merel (dvi, FR), D. Gross (ps, pdf; E), Wolfgang Ruppert (ps.gz, D), Ching-Li Chai (dvi, ps; E; texed by J. Achter), R. Chapman (dvi, ps, pdf; E), I. Fesenko (ps, pdf; E), Jerome Hoffmann (tex, dvi; E), Gregory Sankaran (ps; E).
• Introduction to Algebraic Number Theory by P.Autissier, P.Gollé (dvi.gz, FR)
• Lecture Notes on p-Adic Analytic Number Theory by Ram Murty (dvi, ps; E)
• Examples in Algebraic Number Theory by David Madore (dvi, FR), also available as ps.gz (E)
• Lectures on Diophantine approximation by Wolfgang Ruppert (ps.gz, D)
• Lecture Notes on the Stark Conjectures by D. Hayes (ps, E)
• A book on Galois modules in arithmetics by Boas Erez (dvi, E)
• An introduction to the theory of positive ramification due to K. Wingberg and A. Schmidt by Vincent Secherre (dvi, FR)
• Kubota-Leopoldt L-functions by F.Chapoton, P-H.Chaudouard (dvi.gz, FR)
• History of the main conjecture as proved by Mazur and Wiles by Coates and Poitou (ps.gz, E; transl. from FR by F. Lemmermeyer)
• Arithmetic and Geometry of Salem Numbers by Eknath Ghate (dvi, E)
• Intro to Arakelov geometry by Hugues Randriambolona (dvi.gz, FR)
• Lectures on Euler systems (dvi) by Barry Mazur, with more notes by Tom Weston et al.

Categories

• An introduction to categories by David Madore (dvi, FR), also available as ps.gz (E), Vincent Secherre (dvi, FR)

Class Field Theory

• Lecture notes on Class Field Theory by J.S. Milne (dvi, ps, pdf; E)
• Lecture notes on Computational Class Field Theory by H. Cohen (dvi, E)
• Surveys on class field theory by E. Ghate (dvi, E), Vincent Secherre (dvi, FR), Thomas Shemanske (tex, ps, pdf; E), Matt Baker (dvi, E; also as pdf).
• Surveys of computational class field theory by H. Cohen (dvi, E)

Cohomology of Groups and Sheaves

• Lecture notes on homological algebra by I. Fesenko (ps, pdf; E)
• On Ext and Tor by Sven Blumberg (pdf; D);
• Lecture notes on Sheaves by Günther Trautmann (ps.gz, D) and Olivier Debarre
• Lecture notes on Ringed Spaces by Günther Trautmann (ps.gz, D)
• Cohomology of Groups by N.Singh, I.Marin (dvi.gz, FR)
• Galois Cohomology by J. Tate (tex, dvi, ps.gz; E; texed by H. Verrill and W. Stein)
• Spectral Sequences by Mathias Schulze (ps.gz, D)
• Cohomology of Sheaves by J.Page, R.McDonagh (dvi.gz, FR), Günther Trautmann (ps.gz, D)
• One of the most complete set of notes on cohomology theories by Joel Riou and Yann Ollivier (ps.gz; F)

Commutative Algebra

• Lecture Notes by I. Fesenko (ps, pdf; E), R. Kiehl (ps, D), J. Franke (dvi.gz, D), Wolfgang Ruppert: KA1 (ps.gz, D) and KA2 (ps.gz, D).

Complex Analysis

• Lecture Notes by K. Mathiak 1 (ps, D), K. Mathiak 2 (ps, D),

Complex Multiplication

• Christophe Cornut has a thesis (ps, F) and a paper (ps, E) on a conjecture of Mazur on Heegner points.

Cryptography

• Lecture notes by R. Akhtar (dvi, ps, pdf; E)
• A collection of notes on cryptography by Kapil Hari Paranjape (tex, pdf; E)

RSA
• A quick survey of the RSA cryptosystem by David Madore (dvi, FR), also as ps (FR)

Differential Geometry

• Lecture notes by Bas Edixhoven (ps.gz, FR),
• Abraham, Marsden, Ursula Hamenstädt (ps, D), Sven Blumberg; P. Michor (ps, E)
• online notes by Stefan Waner

Diophantine Geometry

• Lecture Notes on Diophantine Geometry by Wolfgang Ruppert (ps.gz, D)
• Lecture Notes on Heights by Nils-Peter Skoruppa (dvi, ps, pdf; E)
• A habilitation thesis on effective diophantine approximation by Yann Bugeaud.

Elementary Number Theory

• Lecture Notes by David Wilkins (dvi, ps, pdf; E), R. Akhtar (dvi, ps, pdf; E) K. Mathiak 1 (ps, D), K. Mathiak 2 (ps, D), B. Matzat (ps, D), Schnell (zip, D), H. G. Zimmer (ps, D), John Cremona (ps, pdf; E), Franz Lemmermeyer (pdf, E), Nigel Byott (dvi, ps, pdf; E), Bruce Ikenaga (ps, E),

Primality tests from Dublin
Theses
• Liz Foster's senior thesis on cubic and quartic Reciprocity Laws.

Elliptic Curves

• see this page
• Norbert Schappacher deals with the history of the group law on elliptic curves (dvi, F) as well as an article about Diophantus.

Galois Theory

• Lecture notes on Galois Theory by J.S. Milne (dvi, ps, pdf; E), David Wilkins (dvi,ps, pdf; E), Andrew Baker (pdf)
• Lectures on Braids and Galois theory by Frazer Jarvis
• Théorie de Galois (available as dvi, ps and pdf; FR)
• Résumé (available as dvi and ps; FR)
• Finite Fields from Dublin

General Relativity

• bookmarks
• papers
• First Look

Group Theory

• Lecture Notes on Group Theory by J.S. Milne (dvi, ps, pdf; E), David Wilkins (dvi, ps, pdf; E), B. Külshammer (dvi, D)
• Groups, Symmetry and Fractals by Andrew Baker
• Lecture Notes on Finite Groups and their classification by Thomas Keilen (ps.gz, E)
• Lecture Notes on Groups and Geometry by Nils-Peter Skoruppa (ps.gz, FR)
• Lecture Notes on Representation theory by B. Külshammer (dvi, D), Maier (pdf; D) from Dublin, dogschool (html, E) Joel Riou.

Hilbert's Problems

• A list of Hilbert's 23 problems by David Madore (dvi, FR), also as ps.gz (FR)

Langlands Program

• The main websource is of course the one containing lots of Langlands own writings.
• On the web page of A. Raghuram you will find his thesis on representation theory of GL(2,D) over p-adic division algebras D, notes for Ram Murty's Lectures on Artin L-functions and for D. Prasad's Automorphic forms on GL(n) (both dvi).
• The Nonabelian Reciprocity Law for Local Fields by Jonathan Rogawski
• Informal notes by David Ben-Zvi
• Automorphic forms and L-functions
• Vignettes on automorphic and modular forms, representations, L-functions, and number theory
• Marie-France Vigneras
• Mladen Dimitrov on Galois representations and Hilbert modular forms.
• A few things on the subgroups of GL(n,k) by Mathilde Kammerer and Clement Rau
• Introduction to Automorphic L-functions by Ching-Li Chai (dvi, E; texed by J. Achter)

Lie Groups and Lie Algebras

• Lecture notes on Lie groups by Bunke et al. (ps.gz, D), Nils-Peter Skoruppa (ps.gz, FR)
• Intro to Root Systems by Hugues Randriambolona (dvi.gz, FR)

Linear Algebra

• Lecture Notes by Edwin H. Connell (dvi, ps, ps.gz, pdf; E), Oliver Debarre (ps, FR), Dominik Eberlein, Christian Schwarz (ps, D; lectures by Meyberg), Alexei N. Skorobogatov (dvi, E).

Modular Forms and Galois representations

• Lecture notes on Modular Forms by J.S. Milne (dvi, ps, pdf; E), Bas Edixhoven (ps.gz, FR), Frazer Jarvis (dvi, E), Ken Ribet (tex, dvi; E; texed by W. Stein) Marty Weissman (tex, pdf; E); his thesis is about icosahedral Galois representations.
• Lecture Notes on Deformations of Galois Representations by F. Gouvea (dvi, E)
• The Serre conjectures by H. Darmon (dvi, E; also as ps)
• Lecture notes on the Serre conjectures by William Stein, Ken Ribet (dvi, ps, pdf; E)
• On the Shimura-Taniyama Conjecture by H. Darmon (dvi; E; also as ps)
• Introduction to Ramanujan's tau function by S.Bruiltet/E.Gaudron (dvi.gz, FR)
• On congruences involving Ramanujan's tau-function and their interpretation in terms of l-adic representations by Serre (ps, E; transl. from FR by F. Lemmermeyer)
• Nombres p-adiques et représentations de GL₂ by F.Auzende, I.Vidal (dvi.gz, FR)
• Control theorems and applications by H. Hida (dvi, E)

Quadratic Forms

• Quadratic forms over the rational numbers by Vincent Secherre (dvi, FR);

Polylogs

by M. Waldschmidt

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Last modified: Oct 7, 2002 by Franz Lemmermeyer.
• Lecture notes by Paul Garrett
• The CICMA Publications.
• Eine Linksammlung von David Radcliffe.

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