Hodge completed derived de Rham algebra of a perfect ring

Davide Marangoni

Hodge completed derived de Rham algebra of a perfect ring

Algebraic Geometry 2019-06-20 v2 Number Theory

Authors: Davide Marangoni

Abstract

Derived de Rham cohomology has been recently used in several contexts, as in works of Beilinson and Bhatt on p-adic periods morphisms and Morin on numerical invariants for special values of zeta functions. Inspired by some results of Morin, we aimed to compute Hodge completed derived de Rham complex in the case of a rings map $\mathbb{Z}\longrightarrow k$ , factoring through $\mathbb{F}_p$ , with $k$ a perfect ring (i.e. the Frobenius map is an automorphism).

Keywords

derived de rham cohomology hodge completion perfect ring frobenius map p-adic periods rings map

Cite

@article{arxiv.1901.02365,
  title  = {Hodge completed derived de Rham algebra of a perfect ring},
  author = {Davide Marangoni},
  journal= {arXiv preprint arXiv:1901.02365},
  year   = {2019}
}

Comments

It turns out that there is a hole in the crucial proof, so that the actual result of the computation is very different from what we expected. Furthermore the whole paper, with the fixed proof, has become not so much interesting (at the moment)

Hodge completed derived de Rham algebra of a perfect ring

Abstract

Keywords

Cite

Comments

Related papers