597 research outputs found
The Galois group of a stable homotopy theory
To a "stable homotopy theory" (a presentable, symmetric monoidal stable
-category), we naturally associate a category of finite \'etale algebra
objects and, using Grothendieck's categorical machine, a profinite group that
we call the Galois group. We then calculate the Galois groups in several
examples. For instance, we show that the Galois group of the periodic
-algebra of topological modular forms is trivial and that
the Galois group of -local stable homotopy theory is an extended version
of the Morava stabilizer group. We also describe the Galois group of the stable
module category of a finite group. A fundamental idea throughout is the purely
categorical notion of a "descendable" algebra object and an associated analog
of faithfully flat descent in this context.Comment: 93 pages. To appear in Advances in Mathematic
- β¦