Sur une q-déformation locale de la théorie de Hodge non-abélienne en caractéristique positive

Gros, M.

doi:10.1007/978-3-030-43844-9_5

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…This defines the functor (F, F Ω ) * appearing in diagram (1); the hardest part of the following theorem is essential surjectivity, which amount to the existence of a good ϕ(A inf (R))-lattice inside any A inf (R)module with connection. We note that a similar functor, albeit in a rather different context, has also been shown to be an equivalence by Gros-Le Stum-Quirós [21,20].…”

Section: Our Main Class Of Generalised Representations Of Interest Is...mentioning

confidence: 70%

Generalised representations as q-connections in integral $p$-adic Hodge theory

Morrow,

Tsuji

2020

Preprint

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We relate various approaches to coefficient systems in relative integral p-adic Hodge theory, working in the geometric context over the ring of integers of a perfectoid field. These include small generalised representations over A inf inspired by Faltings, modules with q-connection in the sense of q-de Rham cohomology, crystals on the prismatic site of Bhatt-Scholze, and q-deformations of Higgs bundles.

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Section: Our Main Class Of Generalised Representations Of Interest Is...mentioning

confidence: 70%

Generalised representations as q-connections in integral $p$-adic Hodge theory

Morrow,

Tsuji

2020

Preprint

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“…The main result of the present article is the following: we prove (theorem 4.8 and corollary 4.9) that, if A 1 denotes the frobenius pullback of A, then frobenius descent provides an equivalence of categories between A 1 -modules endowed with a twisted connection of level ´1 and A-modules endowed with a twisted connection of level 0 (when we focus on finitely presented topologically quasi-nilpotent objects). Moreover, as we expected in [Gro20], section 6, this is related to prisms via a very general Cartier morphism C, whose definition is inspired by the proof of theorem 16.17 of [BS19], from the q-crystalline topos of a smooth formal scheme X to the prismatic topos of its frobenius pull back X 1 . When X " SpfpA{aq, in which case X 1 " SpfpA 1 {ppq q Aq, there exists a commutative diagram tppq q ´prismatic crystals on X 1 {Ru…”

Section: Introductionmentioning

confidence: 97%

Twisted differential operators of negative level and prismatic crystals

Gros¹,

Stum²,

Quirós³

2020

Preprint

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We introduce twisted differential calculus of negative level and prove a descent theorem: Frobenius pullback provides an equivalence between finitely presented modules endowed with a topologically quasi-nilpotent twisted connection of level minus one and those of level zero. We explain how this is related to the existence of a Cartier operator on prismatic crystals. For the sake of readability, we limit ourselves to the case of dimension one.

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“…This article is the continuation of [GLQ22a] and [GLQ22b]. It is devoted to giving the final arguments realizing our project, first outlined in [Gro20], of putting the local q-twisted Simpson correspondence constructed in [GLQ19] into the perspective of the q-crystalline and prismatic sites theories. These two sites, introduced by Bhargav Bhatt and Peter Scholze in [BS22], and their beautiful properties are the framework allowing the whole picture to take form.…”

Section: Introductionmentioning

confidence: 99%