GEOMETRICALLY IRREDUCIBLE p-ADIC LOCAL SYSTEMS ARE DE RHAM UP TO A TWIST

被引:5
|
作者
Petrov, Alexander [1 ]
机构
[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA
关键词
FUNDAMENTAL-GROUPS; REPRESENTATIONS;
D O I
10.1215/00127094-2022-0027
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We prove that any geometrically irreducible Qp-local system on a smooth alge-braic variety over a p-adic field K becomes de Rham after a twist by a character of the Galois group of K. In particular, for any geometrically irreducible Qp-local system on a smooth variety over a number field the associated projective representa-tion of the fundamental group automatically satisfies the assumptions of the relative Fontaine-Mazur conjecture. The proof uses p-adic Simpson and Riemann-Hilbert correspondences of Diao, Lan, Liu, and Zhu and the Sen operator on the decomple-tions of those developed by Shimizu. Along the way, we observe that a p-adic local system on a smooth geometrically connected algebraic variety over K is Hodge-Tate if its stalk at one closed point is a Hodge-Tate Galois representation. Moreover, we prove a version of the main theorem for local systems with arbitrary geometric monodromy, which allows us to conclude that the Galois action on the proalgebraic completion of net 1 is de Rham.
引用
收藏
页码:963 / 994
页数:32
相关论文
共 50 条
  • [11] Uniformization of p-adic curves via Higgs-de Rham flows
    Lan, Guitang
    Sheng, Mao
    Yang, Yanhong
    Zuo, Kang
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2019, 747 : 63 - 108
  • [12] Local Systems on Diamonds and p-Adic Vector Bundles
    Mann, Lucas
    Werner, Annette
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (15) : 12785 - 12850
  • [13] On irreducible representations of compact p-adic analytic groups
    Ardakov, Konstantin
    Wadsley, Simon
    ANNALS OF MATHEMATICS, 2013, 178 (02) : 453 - 557
  • [14] Limits of residually irreducible p-adic Galois representations
    Khare, C
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (07) : 1999 - 2006
  • [15] Rigidity and a Riemann–Hilbert correspondence for p-adic local systems
    Ruochuan Liu
    Xinwen Zhu
    Inventiones mathematicae, 2017, 207 : 291 - 343
  • [16] p-adic dynamic systems
    Albeverio, S
    Khrennikov, A
    Tirozzi, B
    De Smedt, S
    THEORETICAL AND MATHEMATICAL PHYSICS, 1998, 114 (03) : 276 - 287
  • [17] p-adic dynamic systems
    S. Albeverio
    A. Khrennikov
    B. Tirozzi
    S. De Smedt
    Theoretical and Mathematical Physics, 1998, 114 : 276 - 287
  • [18] p-adic Laplacian in local fields
    Li, Yin
    Qiu, Hua
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 139 : 131 - 151
  • [19] The classification of irreducible admissible mod p representations of a p-adic GLn
    Florian Herzig
    Inventiones mathematicae, 2011, 186 : 373 - 434
  • [20] Local Obstructions at a p-adic Place
    Stix, Jakob
    RATIONAL POINTS AND ARITHMETIC OF FUNDAMENTAL GROUPS: EVIDENCE FOR THE SECTION CONJECTURE, 2013, 2054 : 107 - 117