condensed cohesion

*Speculative page under construction*

Notions of cohesion are generally treated with ∞Grpd as the base (∞,1)-topos. However, for the purposes of algebraic geometry and arithmetic geometry, the (∞,1)-topos of (∞,1)-sheaves over the pro-étale site of a point, $Sh_\infty(ProFinSet)$, may be better suited.

Since this site is used centrally in condensed mathematics, we might call cohesion over this new base, *condensed cohesion*. On the other hand, it is the closed related pyknotic approach that constructs an (∞,1)-topos of pyknotic spaces.

The tangent (∞,1)-topos of $Sh_\infty(ProFinSet)$ ought to be composed of some kind of parameterized spectra. (Pyknotic spectra form the stabilization of the $(\infty, 1)$-category of pyknotic spaces (BarHai19, sec 3.1).)

The big pro-étale site on all schemes over a separably closed field $k$ is almost (check) cohesive over the pro-étale site of a point.

Consider then the construction in cohesive (infinity,1)-topos – structures that do not rely on finite-product preservation in the left adjoint.

The differential cohomology diagram for stable objects in sheaves over the former…

- Clark Barwick, Peter Haine,
*Pyknotic objects, I. Basic notions*, (arXiv:1904.09966)

Last revised on February 22, 2021 at 15:23:55. See the history of this page for a list of all contributions to it.