Dr. Timo Keller

Contact information

Lehrstuhl für Computeralgebra
Mathematisches Institut
Universität Bayreuth
Universitätsstraße 30
95440 Bayreuth, Germany

Zimmer: Gebäude NW II, 3.2.02.737
Telefon: +49-(0)921-55 3384
E-Mail: "Vorname""Punkt""Nachname" "at" uni"Minus"bayreuth"Punkt"de
Lehrstuhl/Arbeitsgruppe: Prof. Dr. Michael Stoll
Sprechstunde: nach Vereinbarung


Research interests

Arithmetic Geometry, especially arithmetic of Abelian schemes, their L-functions and étale, crystalline and flat cohomology, Brauer groups, rational points on varieties over arithmetic fields (also with computational aspects)

Publications

Published

  1. On the Tate-Shafarevich group of Abelian schemes over higher dimensional bases over finite fields, manuscripta math. (2016) 150(1–2), 211–245. DOI: 10.1007/s00229-015-0803-1
  2. A duality theorem for Tate–Shafarevich groups of curves over algebraically closed fields, Abh. Math. Semin. Univ. Hambg. (2018) 88(2), 289–295. DOI: 10.1007/s12188-018-0196-7

Preprints

  1. On an analogue of the conjecture of Birch and Swinnerton-Dyer for Abelian schemes over higher dimensional bases over finite fields 51 pp., submitted
  2. Finiteness properties for flat cohomology of varieties over finite fields 11 pp.
  3. Cohomology operations in Milnor K-theory mod ℓ, transfer of quadratic forms and Stiefel-Whitney invariants 19 pp.

Theses

  1. PhD Thesis (advisor: Uwe Jannsen): The conjecture of Birch and Swinnerton-Dyer for Jacobians of constant curves over higher dimensional bases over finite fields, see also Extended Edition: On the conjecture of Birch and Swinnerton-Dyer for Abelian schemes over higher dimensional bases over finite fields
  2. Diploma Thesis (advisor: Uwe Jannsen): Kohomologieoperationen in Milnor-K-Theorie mod ℓ, Transfer quadratischer Formen und Stiefel-Whitney-Invarianten

Teaching

Wintersemester 2018/2019

Lecture on Brauer groups in arithmetic geometry with exercises, NW II room 3.2.02.740 Monday, Tuesday and Thursday 13:15 s.t.

Topics covered

  1. Crash course in Galois cohomology and Brauer groups of fields
  2. Crash course in étale cohomology and (cohomological) Brauer groups of schemes
  3. Brauer-Manin obstruction, theorems, examples, conjectures

Lectures

  1. Profinite groups, discrete G-modules and infinite Galois theory
  2. Cohomology of profinite groups
  3. Galois cohomology and Brauer groups of fields
  4. Examples of Brauer groups of fields
  5. Milnor K-theory and the theorem of Merkurjev-Suslin
  6. Motivation for étale cohomology
  7. Étale cohomology
  8. Brauer groups of schemes I
  9. Brauer groups of schemes II
References

Exercise sheets

  1. Profinite groups and discrete G-modules
  2. Group and Galois cohomology
  3. Brauer groups of fields
  4. Cohomology of schemes
  5. Zeta functions and the Weil conjectures
  6. Examples for Brauer groups of schemes
  7. Everywhere locally soluble varieties

Activities

Oberseminar Arithmetische Geometrie

Friday, 12:15–13:45 in S82

Kleine AG

Kleine Arbeitsgemeinschaft »Algebraische Geometrie und Zahlentheorie«

Bayerische Kleine AG

Kleine Arbeitsgemeinschaft »Algebraische Geometrie und Zahlentheorie« in Bayern
Next topic: Landweber Exact Functor Theorem (February/March 2019)
Last modified: December 12, 2018
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