p-adic periods and derived de Rham cohomology

By A. Beilinson. 2011

80 citations recorded by the source corpus.

We construct p-adic period map using derived de Rham cohomology of Illusie and give a simple proof of Fontaine's C_{dR} conjecture.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/771df103b870adf6bad3e1d058169a93b5478ace

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Syntomic cohomology and p-adic regulators for varieties over p-adic fields (2013, methodology): “Consider the following commutative diagram with exact rows FmLΩ•Z/S −−−−→ LΩ • Z/S −−−−→ LΩ • Z/S/F my yo yo RuZ/S∗(J [m] Z/S) −−−−→ RuZ/S∗(OZ/S) −−−−→ RuZ/S∗(OZ/S/J [m] Z/S). and use the above theorems of Bhatt and Beilinson.”
$p$ -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES (2012, unknown): “Also, it looks difficult to get results with coefficients using Beilinson’s approach, as the formulation of the condition for a lisse Zp-sheaf to be de Rham seems to be inherently a rigid-analytic condition.”
Cohen-Macaulayness of absolute integral closures (2020, unknown): “ Corollary 3.9. Another consequence of Theorem 3.4 that we shall need is the following, giving a p-adic lift of the main result of [Bha12b] as well as a generalization of [Bha15] (as well as parts of [Bei12]) that accommodates torsion classes and works over a higher dimensional base. Theorem 3.12 (A”
Logarithmic Riemann-Hilbert correspondences for rigid varieties. (2018, background): “ious generalities by diﬀerent methods. When the variety is proper, the trivial coeﬃcient case is contained in the works of Faltings [Fal89, Fal02], Tsuji [Tsu99], Niziol [Niz08, Niz09], and Beilinson [Bei12] (with inputs from Bloch, Fontaine, Hyodo, Kato, Kurihara, and Messing, among others), and th”
On the crystalline period map (2011, methodology): “on theorem [Ill2] Ch. VIII, 2.2.8 due to Olsson [Ol1] 6.10. Let LΩ· (Z,M)/(S,L) be the derived log de Rham complex (we use Gabber’s construction, [Ol1] §8 or [Bh2] §6, to be recalled in a moment; see [B] 3.1 for a short review and the notation used below). This is a commutative dg OS-algebra on Z´et”
Derived Algebraic Geometry (2014, background): “Finally, Bhatt (see [17, 18]), building on Beilinson’s groundbreaking new proof of Fontaine’s CdR conjecture ([12]), has given strikingly short new proofs of the generalized Fontaine-Jannsen Cst and Ccrys, relating the algebraic de Rham cohomology of algebraic varieties over p-adic local fields and ”
Derived algebraic geometry (2014, background): “Finally, Bhatt (see [17, 18]), building on Beilinson’s groundbreaking new proof of Fontaine’s CdR conjecture ([12]), has given strikingly short new proofs of the generalized Fontaine-Jannsen Cst and Ccrys, relating the algebraic de Rham cohomology of algebraic varieties over p-adic local fields and ”
Syntomic complexes and p-adic nearby cycles (2015, background): “Here LΩ XO K,n /OF,n denotes the derived log de Rham complex (see [6] for a review).”