p-adic derived de Rham cohomology

By B. Bhatt. 2012

72 citations recorded by the source corpus.

This paper studies the derived de Rham cohomology of F_p and p-adic schemes, and is inspired by Beilinson's recent work. Generalising work of Illusie, we construct a natural isomorphism between derived de Rham cohomology and crystalline cohomology for lci maps of such schemes, as well logarithmic variants. These comparisons give derived de Rham descriptions of the usual period rings and related maps in p-adic Hodge theory. Placing these ideas in the skeleton of Beilinson's construction leads to a new proof of Fontaine's crystalline conjecture and Fontaine-Jannsen's semistable conjecture.

Subfields: Geometry and Topology, Mathematical Physics, Pharmacology

View Paper: https://www.semanticscholar.org/paper/7bdd83599cd76bdab20970af1ffd6bd81cf5d198

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Citations in the corpus

Derived algebraic geometry (2014, background): “f a more general theorem relating derived de Rham cohomology and algebraic de Rham cohomology in characteristic zero (see [Bhat1]), which itself possesses p-adic and nite characteristic versions (see [Bhat2]). 4.3. Tangent dg-lie algebras. We assume now that kis a base commutative ring of characteri”
On the crystalline period map (2011, methodology): “[Bh1] B. Bhatt, p-divisibility for coherent cohomology, math.”
Syntomic complexes and p-adic nearby cycles (2015, methodology): “n-trivial divisor at inﬁnity treated in Tsuji [65] and Yamashita-Yasuda [68]). Recall that the semistable comparison theorem for schemes was proved also by diﬀerent methods in [26], [27], [47], [48], [9], [7] (see [50] for the proof that most of these methods yield the same period map). They all use”
p-adic periods and derived de Rham cohomology (2011, methodology): “tools arederivedde Rham cohomology of Illusie [Ill2] Ch. VIII and de Jong’s alterations. The companion paper [B] treats the Fontaine-Jannsen side of the story; another approach was developed by Bhatt [Bh2]. It would be very interesting to see if these methods can help to understand the Riemann-Hilbe”
Syntomic cohomology and p-adic regulators for varieties over p-adic fields (2013, methodology): “(r): the mod-pn version of the syntomic complexes S(r) on X K;h . We have the distinguished triangle S n(r) !J[r] cr;n pr ’ ! A cr;n Recall that the ltered Poincare Lemma of Beilinson and Bhatt [4], [8] yields a quasi-isomorphism ˆ cr : J[r] cr;n !˘J[r] cr;n, where J [r] cr ˆA is the r’th ltration l”