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
Algebraic K-Theory
- The book in progress by
Charles Weibel
(dvi; E)
- Matsumoto's calculations for K_{2} 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
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
Complex Analysis
Complex Multiplication
- Christophe Cornut has a thesis (ps,
F) and a paper (ps, E) on a conjecture of Mazur on Heegner points.
Cryptography
RSA
- A quick survey of the RSA cryptosystem by David
Madore (dvi, FR), also as
ps (FR)
Differential Geometry
Diophantine Geometry
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
General Relativity
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
Langlands Program
Lie Groups and Lie Algebras
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 GL_{2} by F.Auzende,
I.Vidal (dvi.gz, FR)
- Control theorems and applications by H. Hida (dvi, E)
Quadratic Forms
Polylogs
Last modified: Oct 7, 2002
by Franz Lemmermeyer.
Lecture notes by Paul
Garrett
The
CICMA Publications.
Eine Linksammlung von David
Radcliffe.