This is a technical problem about applications of Grothendieck topologies. In some recent works, the technique of $h$-topology and $h$-descent is very useful, for an introduction see https://stacks.math.columbia.edu/tag/0ETQ.

However, it seems that such technique is not well-known (for example, there are very few discussions on MathOverflow). What are some good applications of such technique? Some examples are

  • Original work by Voevodsky to study the homology of schemes.
  • Beilinson's approach to p-adic Hodge theory.
  • Bhatt and Scholze's work on projectivity of Witt affine Grassmanian.

And why is $h$-topology and $h$-descent technique useful ? In philosophy, it captures mainly the topological information of schemes (although it's not subcanonical). But I hope to understand more about technical advantages.


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