Topological Hochschild homology and integral p$p$-adic Hodge theory

@article{Bhatt2018TopologicalHH,
  title={Topological Hochschild homology and integral p\$p\$-adic Hodge theory},
  author={Bhargav Bhatt and Matthew T. Morrow and Peter Scholze},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  year={2018},
  volume={129},
  pages={199-310}
}
  • Bhargav Bhatt, Matthew T. Morrow, Peter Scholze
  • Published 2018
  • Mathematics
  • Publications mathématiques de l'IHÉS
  • In mixed characteristic and in equal characteristic p$p$ we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic K$K$-theory by motivic cohomology. Its graded pieces are related in mixed characteristic to the complex AΩ$A\Omega$ constructed in our previous work, and in equal characteristic p$p$ to crystalline cohomology. Our construction of the filtration on THH$\mathrm{THH}$ is via flat descent to semiperfectoid… CONTINUE READING

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