Reduced Whitehead groups of division algebras over function fields of p-adic curves
Event details
| Date | 03.07.2015 |
| Hour | 16:30 › 17:30 |
| Speaker | Prof. Raman Parimala |
| Location | |
| Category | Conferences - Seminars |
The question whether every norm one element of a central simple
algebra is a product of commutators was formulated in 1943 by Tannaka and Artin
in terms of the reduced Whitehead group SK1(D).
For central simple algebras of degree 4, it is a theorem of Merkurjev/Rost that
SK_1(D) is trivial over fields of cohomological dimension 3. This is a consequence
of an injection of SK_1(D) into a subquotient of degree 4 Galois cohomology.
This leads Suslin to ask whether
SK_1(D) is trivial for algebras of indices $l^2$ for a prime $l$
over fields of cohomoogical dimension 3.
In this talk I report on the recent work of Nivedita Bhaskhar on the triviality
of SK_1(D) for period $l$ algebras over function fields of p-adic curves with $l$ not
equal to $p$.
algebra is a product of commutators was formulated in 1943 by Tannaka and Artin
in terms of the reduced Whitehead group SK1(D).
For central simple algebras of degree 4, it is a theorem of Merkurjev/Rost that
SK_1(D) is trivial over fields of cohomological dimension 3. This is a consequence
of an injection of SK_1(D) into a subquotient of degree 4 Galois cohomology.
This leads Suslin to ask whether
SK_1(D) is trivial for algebras of indices $l^2$ for a prime $l$
over fields of cohomoogical dimension 3.
In this talk I report on the recent work of Nivedita Bhaskhar on the triviality
of SK_1(D) for period $l$ algebras over function fields of p-adic curves with $l$ not
equal to $p$.
Practical information
- Informed public
- Free
Organizer
- Prof. Eva Bayer
Contact
- Natascha Fontana