2024 Untilting line bundles on perfectoid spaces

Untilting line bundles on perfectoid spaces

Author: hlzl

August undefined, 2024

WebDec 14, 2024 · Ben Heuer. For a smooth rigid space over a perfectoid field extension of , we investigate how the -Picard group of the associated diamond differs from the analytic Picard group of . To this end, we construct a left-exact "Hodge--Tate logarithm" sequence. We deduce some analyticity criteria which have applications to -adic modular forms. 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.

[2012.07918] Line bundles on rigid spaces in the $v$-topology

WebPERFECTOID 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 WebDec 14, 2024 · Ben Heuer. For a smooth rigid space over a perfectoid field extension of , we investigate how the -Picard group of the associated diamond differs from the analytic … bostock shelter trimmer

[PDF] The number of ramified covering of a Riemann surface by …

Web3. Untilting Line Bundles on Perfectoid Spaces Gabriel Dorfsman-Hopkins (University of California, Berkeley) Let be a perfectoid space with tilt . IT was build a natural map where the (inverse) limit is taken over the -power map, and show that is an isomorphism if is a perfectoid ring. As a consequence we obtain WebFeb 8, 2024 · Untilting Line Bundles on Perfectoid Spaces. Let X be a perfectoid space with tilt X. We build a natural map θ : PicX → limPicX where the (inverse) limit is taken over the … http://www.gabrieldorfsmanhopkins.com/files/projectivoidgeometry.pdf hawkesbury after hours clinic

Line bundles on rigid spaces in the v-topology

Advances in Mixed Characteristic Commutative Algebra

WebNov 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, … http://math.stanford.edu/~conrad/Perfseminar/refs/perfectoid.pdf hawkesbury afloat boat hireWebAs 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. bostock social club

"WebWhen will the Picard groups of a perfectoid space Xand its tilt X[be isomorphic? Does every nite rank vector bundle on the projectivoid line split as a direct sum of line bundles? As we will see in this work, these all naturally lead to the following question. Question 1.0.3. For X=Kproper, where Kis a nontrivially-valued nonarchimedean " - Untilting line bundles on perfectoid spaces

Untilting line bundles on perfectoid spaces

Linebundlesonperfectoidcovers: caseofgoodreduction - arXiv

WebDepartment of Mathematics, University of California San Diego ***** Math 209 - Number Theory Seminar WebLet be a perfectoid space with tilt . We build a natural map where the (inverse) limit is taken over the -power map, and show that is an isomorphism if is a perfectoid ring. As a consequence we obtain a characteriz…

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Webcan 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 … 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 …

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. WebFeb 8, 2024 · perfectoid cover of projective space and p erfectoid covers of toric varieties where the analogous map is an isomorphism ([DH19, Theorem 3.4] and [DHRW2 0, …

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. 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 …

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 …

WebAlso, 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; bostocks toursWebMay 11, 2024 · Untilting Line Bundles on Perfectoid Spaces. Article. Nov 2024; ... S. Das. Vector Bundles on Perfectoid Spaces. PhD thesis, UC San Diego, 2016. Projective … hawkesbury aged care salisbury northWebTo 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 … hawkesbury aged careWebMay 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 … bostocks day trips congleton hawkesbury activitiesWebNov 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 ... bostock shoesWebApr 12, 2024 · Untilting Line Bundles on Perfectoid Spaces. Gabriel Dorfsman-Hopkins; Mathematics. 2024 … Expand. 1. PDF. Save. Alert. Line bundles on perfectoid covers: … bostock smith