Untilting line bundles on perfectoid spaces

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August undefined, 2024

WebA perfectoid field is a complete topological field K whose topology is induced by a nondiscrete valuation of rank 1, such that the Frobenius endomorphism Φ is surjective on … WebK[, we can chain this together with the correspondence of line bundles and maps to projectivoid space to compare line bundles on Xand X[. The main result follows. Theorem …

[PDF] Perfectoid covers of abelian varieties Semantic Scholar

WebThe Hurwitz space is a compactification of the space of rational functions of a given degree. The Lyashko-Looijenga map assigns to a rational function the set of its critical values. It is known that the number of ramified coverings of CP^1 by CP^1 with prescribed ramification points and ramification types is related to the degree of the Lyashko--Looijenga map on … http://www-personal.umich.edu/~stevmatt/perfectoid2.pdf how to make folder in outlook with rules

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http://math.stanford.edu/~conrad/Perfseminar/refs/perfectoid.pdf WebNov 21, 2011 · Abstract. We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings' almost purity theorem, and for which there is a natural tilting ... WebFeb 8, 2024 · Donate to arXiv. Please join the Simons Foundation and our generous member organizations in supporting arXiv during our giving campaign September 23-27. 100% of … how to make folder names bold in outlook

Line bundles on perfectoid covers: case of good reduction

[2102.04354] Untilting Line Bundles on Perfectoid Spaces

WebUntilting Line Bundles on Perfectoid Spaces. by Gabriel Dorfsman-Hopkins. Functionalities for genus 2 and 3 curves. by Reynald Lercier. On the abundance theorem for numerically trivial canonical divisors in positive characteristic. by Sho Ejiri. The slope of fibred surfaces: unitary rank and Clifford index. WebA perfectoid field is a complete topological field K whose topology is induced by a nondiscrete valuation of rank 1, such that the Frobenius endomorphism Φ is surjective on K °/ p where K ° denotes the ring of power-bounded elements. Perfectoid spaces may be used to (and were invented in order to) compare mixed characteristic situations with ... how to make folder in microsoft wordWebPERFECTOID SPACES 249 R n-algebra which is étale after inverting p, and one deﬁnes S m as the integral closure of R m in (S n ⊗ Rn R m)[p−1]for m ≥n, then the direct limit S∞ of the S m is almost ﬁnite étale over R∞.IfonedeﬁnesS=S n ⊗ Rn R, then S is ﬁnite étale over R, and our version of the almost purity theorem says that S is almost ﬁnite étale over R =Rˆ how to make folder link in email

"WebAs our ﬁrst application of Theorem 1.2, we deduce several useful criteria for telling whether a v-line bundle is analytic, that is, descends to a line bundle in the analytic topology. Corollary 1.4. Let L be a v-line bundle on X. Let 𝑉⊆𝑋be any Zariski-dense analytic open subspace. Then L is analytic if and only if 𝐿 𝑉is analytic. " - Untilting line bundles on perfectoid spaces

Untilting line bundles on perfectoid spaces

[1111.4914] Perfectoid spaces - arXiv.org

WebMay 11, 2024 · We use our results to answer some general questions about Picard groups and Picard functors of perfectoid spaces, ... This is part III of a series on line bundles on … Webthe notion of a perfectoid K-space, built by glueing together “spectra” of perfectoid K-algebras, has been deﬁned. The main theorem concerning these objects is: Theorem 2 …

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WebNov 21, 2011 · Perfectoid spaces. Peter Scholze. We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings' almost purity theorem, and for which there is a natural tilting operation which exchanges characteristic 0 and characteristic p. We deduce the weight-monodromy conjecture in certain cases by ... WebPub Date: February 2024 DOI: 10.48550/arXiv.2102.04354 arXiv: arXiv:2102.04354 Bibcode: 2024arXiv210204354D Keywords: Mathematics - Algebraic Geometry;

WebApr 21, 2024 · As a first example, one can use the perfectoid Tate algebra to define analogues of projective spaces in the category of perfectoid algebras; these play an … WebMay 11, 2024 · Line bundles on perfectoid covers: case of good reduction. Ben Heuer. We study Picard groups in profinite perfectoid limits of rigid spaces in the case of good …

WebMay 9, 2024 · Gabriel Dorfsman-Hopkins, Untilting Line Bundles on Perfectoid Spaces, Advances in Mixed Characteristic Commutative Algebra and Geometric Connections, … WebFeb 8, 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

WebFor proper smooth rigid spaces X in characteristic 0, we have seen in [28, Theorem 1.1] that the ´etale Picard functor deﬁned on perfectoid test objects is the diamondiﬁcation of the rigid analytic Picard functor. We had used this to characterise line bundles on X that are trivialised by pro-ﬁnite-´etale covers. how to make folder roblox studioWebTo understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. We develop a perfectoid analog of projective geometry, and explore how equipping a perfectoid space with a map to a certain analog of projective space can be a … how to make folder name emptyWebcan associate line bundles on X♭ to maps to a perfectoid analog of projective space using [DH19, Theorem 4.6] which in turn are in one-to-one correspondance for X and X ♭ by the … how to make folders and subfolders in outlookWebNov 20, 2024 · In the final section, we apply these results to describe an example of a perfectoid cover of an abelian variety over $\bC _p$ with good reduction, … how to make folders for filesWebMay 11, 2024 · Line bundles on perfectoid covers: case of good reduction. Ben Heuer. We study Picard groups in profinite perfectoid limits of rigid spaces in the case of good reduction. Our main result is that for sufficiently large covers, these can be described in terms of the special fibre: For example, our description implies that for a supersingular ... how to make folders for documents savedWebAlso, if Ais of characteristic p, then the untilting map # : A[!Ais an isomorphism of rings. Lemma 1.7. Let Abe an integral perfectoid ring. Then: (i)the untilting map # : A[!Ais continuous; (ii)the isomorphisms of monoids lim x7!x p A!A[= lim x7!xp A=pA!lim x7!x A=ˇAare homeomorphisms, where ˇ2Ais any perfectoid pseudo-uniformiser; how to make folders fire hd 10WebApr 12, 2024 · Untilting Line Bundles on Perfectoid Spaces. Gabriel Dorfsman-Hopkins; Mathematics. 2024 … Expand. 1. PDF. Save. Alert. Line bundles on perfectoid covers: … how to make folders in file explorer