Shauly Ragimov (U Chicago): Universality of character theory
- Event Type
- Seminar/Symposium
- Sponsor
- UIUC Math Department
- Location
- Altgeld 243
- Date
- Oct 28, 2025 11:00 am
- Views
- 66
- A key tool in the computation of En-cohomology of π-finite spaces is the transchromatic character, constructed by Hopkins-Kuhn-Ravenel and extended by Stapleton and Lurie. For each 0 ≤ (n − t) ≤ n, the height (n − t)-transchromatic character relates the En-cohomology of a π-finite space to that of its (n − t)-fold p-typical loop space, evaluated with respect to a height t-cohomology theory.
We place this construction into a unified framework of (n − t)-fold character theories ap- plicable to any ∞-commutative monoid. Concretely, for an ∞-commutative monoid R there is a universal (n − t)-fold character map that respects the natural induction and restriction structures of R. In particular, it yields a character theory for every T(n)-local algebra. This universal character enjoys strong structural properties: it exhibits a blue-shift phenomenon by sending T(n)-local algebras to T(t)-local algebras, and it carries primitive height-n roots of unity to primitive height-t roots of unity. In the case of En, it recovers the classical transchro- matic character.