2021
DOI: 10.4171/jems/1116
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Projective crystalline representations of étale fundamental groups and twisted periodic Higgs–de Rham flow

Abstract: This paper contains three new results. (1) We introduce new notions of projective crystalline representations and twisted periodic Higgs–de Rham flows. These new notions generalize crystalline representations of étale fundamental groups introduced by Faltings [Algebraic Analysis, Geometry, and Number Theory (1989)] and Fontaine and Laffaille [Ann. Sci. Éc. Norm. Supér. (4) 15 (1983)] and periodic Higgs–de Rham flows introduced by Lan, Sheng and Zuo [J. Eur. Math. Soc. (JEMS) 21 (2019)]. We establish an equival… Show more

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Cited by 6 publications
(6 citation statements)
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“…We confirmed this conjecture via explicit computation for cases that the characteristic p ≤ 50, see [SYZ17] Note that self-maps on P 1 descended from n-multiplication by maps on an elliptic curve π : E → P 1 (n ∈ Z) are called Lattès maps ([Mil06]). If we vary λ ∈ P 1 \ {0, 1, ∞}, we obtain a family of self-maps ψ λ .…”
Section: Conjecture 11 ( [Syz17]mentioning
confidence: 54%
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“…We confirmed this conjecture via explicit computation for cases that the characteristic p ≤ 50, see [SYZ17] Note that self-maps on P 1 descended from n-multiplication by maps on an elliptic curve π : E → P 1 (n ∈ Z) are called Lattès maps ([Mil06]). If we vary λ ∈ P 1 \ {0, 1, ∞}, we obtain a family of self-maps ψ λ .…”
Section: Conjecture 11 ( [Syz17]mentioning
confidence: 54%
“…In [SYZ17] one considers rank-2 stable logarithmic Higgs bundles over the projective line (P 1 , S) with n punctures and with the parabolic structure attached to one puncture in S of weight {1/2, 1/2}. The moduli space HIG contains irreducible components of dimensions n − 3, n − 5, n − 7, • • • .…”
Section: Ii1 P-adic Simpsonmentioning
confidence: 99%
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“…In [SYZ,Section 2] the authors extend Fontaine-Laffaille-Faltings' functor D so that they are able to obtain some projective representations of π ét 1 (X ⊗ W K)…”
Section: Crystalline Representations Of the éTale Fundamental Groupmentioning
confidence: 99%
“…Conjecture 0.6 (Sun-Yang-Zuo [SYZ17]). The self-map induced by Higgs-de Rham flow on M gr 1 2 Higλ over F q comes from multiplication map by p on the associated elliptic curve over…”
Section: Introductionmentioning
confidence: 99%