2024 Hodge tate spectral

Hodge tate spectral

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August undefined, 2024

Nettet19. okt. 2024 · Hodge-Tate spectral sequence [1]. First, we address the connection to Ho dge-Tat e local systems. Second, we establish the functoriality of the p -adic Simpson correspondence by proper direct Nettet11. apr. 2024 · We establish a connection between continuous K-theory and integral cohomology of rigid spaces. Given a rigid analytic space over a complete discretely valued field, its continuous K-groups vanish in degrees below the negative of the dimension. Likewise, the cohomology groups vanish in degrees above the dimension. The main …

A NOTE ON HODGE-TATE SPECTRAL SEQUENCES - ResearchGate

NettetIn particular, the di erentials in the Hodge-Tate spectral sequence Hs(X i; r X i=W(k)) )Hs+r(X i=W(k)[[u]]) vanish modulo torsion. But, as we established above, the Hodge cohomology of X i has no torsion, so the Hodge-Tate spectral sequence degenerates at the second page. Therefore the conjugate spectral sequence for X Netteton the geometry of the Hodge-Tate period map. In particular, we compare the bres of the Hodge-Tate period map with Igusa varieties. Contents 1. Introduction 2 2. Re ning the Hodge-Tate period map 10 2.1. Recollections on the Hodge-Tate period map 10 2.2. The p-adic-de Rham comparison isomorphism 13 2.3. Hodge cycles and torsors 16 3. paper towel sniffer job

A NOTE ON HODGE-TATE SPECTRAL SEQUENCES - arXiv

Nettetsmooth rigid-analytic space Xover C, the Hodge-to-de Rham spectral sequence Eij 1 = H j(X; i X) )H i+j dR (X=C) degenerates at E 1. Moreover, for all i 0, Xi j=0 dim CH i j(X; j … NettetCorrection: The affiliation of Lei Fu is Tsinghua University.I will report on a joint work with Michel Gros providing a generalization of the Hodge-Tate spec... Nettet8. mar. 2024 · Along the way, we establish various foundational results on the geometry of the Hodge-Tate period map. In particular, we compare the fibres of the Hodge-Tate … paper towel single fold 230 x 220 mm

The p -adic Corlette–Simpson correspondence for abeloids

NettetIt is well known that the p-adic étale cohomology of a smooth and proper variety over a p-adic field admits a Hodge-Tate decomposition and that it is the abutment of a spectral sequence called Hodge-Tate; these two properties are incidentally equivalent. Nettet20. jun. 2024 · We prove that the Hodge-Tate spectral sequence of a proper smooth rigid analytic variety can be reconstructed from its infinitesimal -cohomology through the … paper towel single fold 230x220mm 100\u0027shttp://shizhang.li/papers/integral%20Hodge%20filtration.pdf paper towel sheet weight

"Nettet3. p-adic Hodge theory 13 3.1. Introduction 13 3.2. A comparison result for constructible coe cients 17 3.3. The Hodge-Tate spectral sequence 20 4. A p-adic analogue of … " - Hodge tate spectral

Hodge tate spectral

INTEGRAL p-ADIC HODGE FILTRATIONS IN LOW DIMENSION …

NettetThe Hodge-Tate spectral sequences play an important role in some of the recent breakthroughs in arithmetic geometry, namely it is used to de ne Hodge-Tate period … NettetThe analogous p-adic Hodge theory of p-adic algebraic varieties was initiated by Tate in the 1960s and subsequently completed by Fontaine-Messing, Faltings, Kato, Tsuji, Niziol and Beilinson. Tate asked in his original paper whether the theory worked not only for p -adic varieties but for the wider class of p -adic rigid-analytic spaces, which are the p …

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Nettet8. mar. 2024 · The relative Hodge-Tate spectral sequence -- an overview A. Abbes, Michel Gros Published 8 March 2024 Mathematics arXiv: Algebraic Geometry We give in this note an overview of a recent work leading to a generalization of the Hodge-Tate spectral sequence to morphisms. NettetA NOTE ON HODGE-TATE SPECTRAL SEQUENCES 3 Remark 1.3. The B+ dR-lattices in H i et (X;Q p) Qp B dR are parameterized by the C-points of B dR-a ne Grassmannian GrB dR GLn as de ned in [CS17] de ...

NettetHodge-Tate spectral sequence to morphisms of singular varieties. If one would like to be more optimistic about the site I S → S , then it is interesting to lo ok for an intrinsic pr … Nettet11. jun. 2024 · On the other side, we consider the "Hodge-Tate cohomology" of X. This is: HkHT(X / K) = ⨁ i + j = kHi(X, ΩjX / K) It is a graded K -vector space with grj HkHT(X / …

Nettet11. sep. 2015 · Abstract The Hodge-Tate spectral sequence for a proper smooth variety over a p-adic field provides a framework for us to revisit Faltings' approach to p-adic … NettetIn p-adic Hodge theory, the analogous concept to complex Hodge decomposition (HS) is the p-adic Hodge-Tate (HT) decomposition. An HT structure also represents the absolute Galois group of the ground p-adic ﬁeld. Besides, both decompositions above can be equally described through the convergence of the Hodge to de Rham spectral sequence.

Nettetthe Hodge-Tate spectral sequence to morphisms. The latter takes place in Faltings topos, but its construction requires the introduction of a relative variant of this topos which is …

Nettet21. des. 2024 · There is a related notion of the Shafarevich-Tate group associated to a Lagrangian fibration. Its connected component of unity can be shown to be isomorphic to $\mathbb C/\Lambda$ where $\Lambda$ is a finitely generated subgroup of $\mathbb C$ and $\mathbb C$ is thought of as the base of the Shafarevich-Tate family. paper towel smooth icingNettet5. Hodge-Tate decomposition of abelian varieties 14 References 18 1. Foreword This survey presents the theory of Hodge-Tate decompositions of etale cohomology groups … paper towel spilled drinkNettet8. mar. 2024 · This is canonical after choices of an exponential on K and of a splitting of the Hodge–Tate sequence of A.. Here pro-finite-étale Higgs bundles are defined as Higgs bundles such that the underlying vector bundle becomes trivial on a pro-finite-étale covering of A.. To motivate the theorem, we recall that the complex Corlette–Simpson … paper towel stand blackNettet8. mar. 2024 · This book presents two important results in p-adic Hodge theory following the approach initiated by Faltings, namely (i) his main p-adic comparison theorem, and (ii) the Hodge-Tate spectral sequence. We establish for each of these results two versions, an absolute one and a relative one. paper towel slow cookerNettet20. jun. 2024 · PDF We prove that the Hodge-Tate spectral sequence of a proper smooth rigid analytic variety can be reconstructed from its infinitesimal... Find, read … paper towel stock imageNettetintroduces a non-trivial di erential in the Hodge-de Rham spectral sequence. In particular, X is non-Kähler. 2 p-adic Hodge Theory 2.1 Hodge-Tate decomposition p-adic Hodge theory is about an analogue of these results for manifolds over p- adic ﬁelds (discretely valued, complete non-archimedean extension of Q p with perfect residue ﬁeld k) paper towel stock photoNettetIn mathematics, a Hodge–Tate module is an analogue of a Hodge structure over p-adic fields. Serre introduced and named Hodge–Tate structures using the results of Tate on … paper towel square footage chart