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2. Two Towers Isomorphism

The two towers isomorphism is a $\text{GL}_n(\mathbf{Q}_p) \times D_{1/n}^\times$-equivariant isomorphism of perfectoid spaces $$\text{LT}_{n,\infty} \cong \mathcal{H}^{n-1}_\infty,$$ where $\mathcal{H}^{n-1}$ is Drinfeld symmetric space in dimension $n -1$.


    1. Add remark

      Problem 2.1.

      This isomorphism can be understood in terms of the respective moduli problems when evaluated on perfectoid rings. Is there a geometric description of the two tower isomorphism for more general rings?


        • Add remark

          Problem 2.2.

          Is there a way to enhance the two tower isomorphism in terms of analytic stacks?

              Cite this as: AimPL: Chromatic homotopy theory and p-adic geometry, available at http://aimpl.org/chromhomotopy.