Structural properties of equivariant and motivic stable homotopy categories

点击翻译按钮获取中文摘要

We will study certain structural properties of the motivic stable homotopy category SH(k) over a given base field k as introduced by Morel and Voevodsky [MV], also called the stable A1-homotopy category. In particular, we wish to establish motivic generalizations of the famous classification results concerning thick subcategories as established by Hopkins and Smith [HS] within their work on nilpotence in stable homotopy. This would be a very big theorem, as so far there does not even exist a precise conjecture of how this classification might look like in the motivic case. What does exist are various suggestions for the construction of motivic versions of Morava K-theories, which in the classical case play a crucial role. As a first step, we wish to proceed towards a classification of thickideals in the G-equivariant stable homotopy category localized at a given prime p for some (e. g. finite cyclic) groups. There are some partial results in this direction (see below) due to Strickland [S2], which show that this certainly is a promising research project.