Mathematisches Institut Georg-August-Universität Göttingen |
![]() |
Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry" Recorded Lessons |
Windows: | Please download the latest XviD-Codec from www.koepi.org/xvid.shtml |
MacOS X: |
by default the QuickTime-plugin doesn't know how to handle the
XviD-format. There are two possibilities to use XviD with Quicktime:
|
Linux: |
Please consult Your package-manager to download the lates
XviD-package Usually the codec gets installed with any media player. |
Week 1 |
July 17 |
July 18 |
July 19 |
July 20 |
July 21 |
|
10:00 |
Y. Tschinkel Introduction |
Y. Tschinkel Hypersurfaces |
Y. Tschinkel Toric varieties I |
Y. Tschinkel Toric varieties II |
Y. Tschinkel Flag varieties |
11:30 |
B. Hassett Rational surfaces over algebraically closed fields |
B. Hassett Rational surfaces over non-closed fields I |
B. Hassett Rational surfaces over non-closed fields II |
B. Hassett Singular Del Pezzo surfaces |
B. Hassett Cox rings and universal torsors |
14:30 |
A. Kresch Brauer groups, Galois cohomology |
A. Kresch Brauer-Manin obstruction with quaternion algebras |
A. Kresch Descent, torsors |
A. Kresch Hasse principle and Brauer-Manin obstruction |
A. Kresch Further examples |
16:00 |
S. Wiedmann Introduction to computers at the MI |
G. Pfister |
J. Jahnel Rational points on hypersurfaces |
M. Stoll Computations with genus 2 curves |
M. Stoll Computations with genus 2 curves II |
17:30 |
BBQ |
Exercises |
Exercises |
Exercises |
Exercises |
Week 2 |
July 24 |
July 25 |
July 26 |
July 27 |
July 28 |
|
10:00 |
H. Darmon Arithmetic of curves: overview |
H. Darmon Faltings' theorem I |
H. Darmon Faltings' Theorem II |
H. Darmon Modular curves and Mazur's Theorem |
M. Rebolledo Merel's theorem, continued |
11:30 |
J. Starr Tsen-Lang theorem |
J. Starr Arithmetic over function fields of curves |
J. Starr Arithmetic over function fields of surfaces |
D. Harari Bielliptic surfaces |
D. Harari Enriques surfaces |
14:30 |
C. Popescu Special values of L-functions |
Y. Tschinkel Compactifications of additive groups |
D. Harari Nonabelian descent |
M. Rebolledo Merel's theorem |
F. Bogomolov Geometry over small fields |
16:00 |
H. Chapdelaine The generalised Fermat equation |
B. Moroz Circle method I |
S. Wiedmann Zeta functions of regular graphs |
B. Moroz Circle method II |
H. Darmon Fermat curves and Wiles' Theorem |
17:30 |
Exercises |
Exercises |
Exercises |
Exercises |
Exercises |
Week 3 |
July 31 |
August 1 |
August 2 |
August 3 |
August 4 |
|
10:00 |
H. Darmon Elliptic curves and modular forms |
H. Darmon The theorems of Gross-Zagier and Kolyvagin |
H. Darmon Proof of Kolyvagin's Theorem |
H. Darmon p-adic uniformisation |
H. Darmon Stark-Heegner points |
11:30 |
D. Abramovich Geometry and arithmetic of curves |
D. Abramovich Kodaira dimension |
D. Abramovich Campana's program |
D. Abramovich The minimal model program |
D. Abramovich Vojta, Campana and ABC |
14:30 |
A. Chambert-Loir Equidistribution on the projective line |
J. Voight Some diophantine applications of Heegner points |
A. Chambert-Loir Arakelov geometry and equidistribution |
M. Greenberg Calculating Heegner points via overconvergent modular symbols |
A. Chambert-Loir Equidistribution on Berkovich spaces |
16:00 |
N. Elkies Newton iteration for simultaneous algebraic equations |
O. Labs Construction of hypersurfaces with singularities |
J. Voight Shimura curve computations |
J. Schicho Construction of rational points on rational surfaces |
M. Greenberg Elliptic curves over imaginary quadratic fields |
17:30 |
Exercises |
Exercises |
Exercises |
Exercises |
Exercises |
Week 4 |
August 7 |
August 8 |
August 9 |
August 10 |
August 11 |
|
10:00 |
F. Oort Introduction: Density of Hecke orbits |
F. Oort The Tate-conjecture |
F. Oort A conjecture of Manin and the weak Grothendieck conjecture |
F. Oort Purity and deformations of p-divisible groups |
F. Oort Proof of the density of ordinary Hecke orbits |
11:30 |
C.-L. Chai Serre-Tate theory |
C.-L. Chai Dieudonné and Cartier modules |
C.-L. Chai Hilbert modular varieties |
B. Poonen Varieties over finite fields II |
C.-L. Chai Proof of the Grothendieck conjecture |
14:30 | E. Ullmo The André-Oort conjecture and Manin-Mumford |
B. Poonen Varieties over finite fields I |
E. Ullmo Equidistribution of special varieties |
Yu. I. Manin Iterated modular symbols II |
Yu. I. Manin Iterated modular symbols III |
16:00 |
W.
Messing (ca. 800 MB) Theory of displays I |
W.
Messing (ca. 750 MB) Theory of displays II |
Y. I. Manin Iterated modular symbols I | D. Kaledin Cartier isomorphism I | D. Kaledin Cartier isomorphism II |