nLab Ambidexterity in K(n)-Local Stable Homotopy Theory


This page collects some links related to

on bilimits in K(n)-local stable homotopy theory and generally on ambidextrous adjunctions and their un-twisted Wirthmüller isomorphisms for ∞-module bundles in semiadditive (∞,1)-categories.

(The untwisted Wirthmüller isomorphism is the map μ\mu in Construction 4.0.7 and then the norm map in Remark 4.1.12. The induced integration map considered in Construction 4.0.7, Notation 4.1.6 there is also discussed (for the general twisted case) in the article Quantization via Linear homotopy types, see section 4.3 there for details.)

The discussion in the article is apparently motivated as part of what it takes to make precise the discussion of quantization in sections 3 and 8 of

For the 2014 installment of UOregon’s Moursund Lecture Series, Jacob Lurie gave three (video recorded) lectures on spectral algebraic geometry, one of which is


1. Multiplicative aspects of Dieudonne Theory

2. The Morava KK-theory of Eilenberg-MacLane Spaces

3. Alternating powers of pp-Divisible groups

4. Ambidexterity

4.1 Beck-Chevalley fibrations and Norm maps

4.2 Properties of the norm

4.3 Local systems

4.4 Examples

5. Ambidexterity of K(n)K(n)-Local stable homotopy theory

5.1 Ambidexterity and duality

5.2 The main theorem

5.3 Cartier duality

5.4 The global sections functor

category: reference

Last revised on May 1, 2023 at 10:08:17. See the history of this page for a list of all contributions to it.