Prof. Dr. Jens Franke
Lecture "Etale Cohomology" WS23/24
The lecture is currently scheduled for Thursdays 14-16ct in 0.006 and
Fridays 16-18ct in Zeichensaal.
The etale site will be introduced and the basic results on which the proof
of the Weil conjectures depends, like proper and smooth base change, will be
covered. This will be followed by a lecture on Weil 1 next year.
A very good knowledge of algebraic geometry 1/2 will be required.
Exams will be written on Friday, February 16, 2024 and Monday, March 18,
2024 from 9 to 12 (s. t.) in Kleiner Hörsaal (Wegelerstr. 10).
Lecture "Real algebraic geometry: The real spectrum"
The lectures will be on Tuesdays 8-10ct and Fridays 10-12ct in 0.006.
After an introduction to real closed fields the real spectrum will be
introduced and a result of Coste and Roy generalizing the real quantifier
elimination result of Tarski and Seidenberg will be shown. A good knowledge
of basic ring theory as well as Galois theory and some familiarity with the
ordinary prime ideal spectrum will be required, but apart from this the
prerequisites from algebra are minimal. The required results about spectral
spaces will be introduced and shown in the lecture.
Exams will be written on Tuesday, February 6, 2024 and Thursday, March 14,
2024 from 9 to 12 (s. t.) in Kleiner Hörsaal (Wegelerstr. 10).
Exercise sheets:
- Exercise 1, due October 20
(pdf)
- Exercise 2, due October 25
(pdf)
- Exercise 3, due November 3
(pdf)
- Exercise 4, due November 10
(pdf)
- Exercise 5, due November 17
(pdf)
- Exercise 6, due November 22
(pdf)
- Exercise 7, due November 29
(pdf)
- Exercise 8, due December 8
(pdf
- Exercise 9, due December 20
(pdf)
- Exercise 10, due January 10
(pdf)
- Exercise 11, due January 12
(pdf)
- Exercise 12, due January 17
(pdf)
Sprechstunden
In der vorlesungsfreien Zeit sind die Sprechstunden nach Vereinbarung.
Vorlesungen "Mathematik für Physiker I-III"
Die Javascript-Programme zu den Anwesenheitsübungen dieser Vorlesungen, die
ich zwischen 2008 und 2011 gehalten habe, sind weiterhin online:
Selected Publications
- On the spaces Fspq of Triebel-Lizorkin type:
pointwise multipliers and spaces on domains, Math. Nachr. 125 (1986),
113-149.
- (with Yu. I. Manin and Yu. Tschinkel)
Rational points of bounded height on Fano varieties,
Invent. Math. 95(1989), 421-435
- (with T. Runst)
Regular elliptic boundary value problems in Besov-Triebel-Lizorkin spaces.
Math. Nachr. 174 (1995), 113-149.
- Harmonic analysis in weighted L2-spaces,
Ann. Sci. École Norm. Sup. (4), 31(1998), 181-279
- (with J. Schwermer),
A decomposition of spaces of automorphic forms, and the Eisenstein
cohomology of arithmetic groups,
Math. Ann. 311(1998), 765-790.
- On the singularities of residual Eisenstein series,
Invent. Math. 138(1999), 307-317
- (With T. Kleinjung, F. Morain and T. Wirth)
Proving the primality of very large numbers with fastECPP,
in Algorithmic number theory,
Lecture Notes in Comput. Sci., 3076, 2004, pages 194-207.
- (With T. Kleinjung),
Continued fractions and lattice sieving.
In: Proceedings SHARCS 2005
- (with K. Aoki, T. Kleinjung, A. Lenstra, D. Osvik)
A kilobit special number field sieve factorization,
in Advances in cryptology. ASIACRYPT 2007,
Lecture Notes in Comput. Sci., 4833, 2007, pages 1-12.
- A topological model for some summand of the Eisenstein
cohomology of congruence subgroups, in
Eisenstein series and applications, Progr. Math., 258, 2008,
pages 27-85.