*Time: *Friday, January 28, 2011,
17h30-18h30

## Canonical dimension of algebraic tori

**Roland Loetscher **
(Munich - Personal website)

Canonical dimension is a numerical invariant of algebraic varieties X over a field F, that measures how far X is from having a F-rational point. This concept has been introduced in 2005 by G. Berhuy and Z. Reichstein, and was recently presented at ICM 2010 by N. Karpenko. In the first part of the talk I want to give you an idea of canonical dimension and to show how it is related to essential dimension. In the second part I will present a general result on canonical dimension, where the varieties in question are torsors of a given algebraic F-torus. As an application we get the following statement: Let p be a prime integer and let T be an anisotropic F-torus which splits over a cyclic extension of p-primary degree. Then T admits a torsor (over some field extension of F) whose canonical dimension is equal to the (usual) dimension of T.