Fargues-scholze

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August undefined, 2024

http://math.bu.edu/people/jsweinst/rampage/Hemo.pdf WebCOMPATIBILITY OF THE FARGUES-SCHOLZE AND GAN-TAKEDA LOCAL LANGLANDS 5 B(GL n) isanelementintheKottwitzsetof GL n correspondingtoarank nisocrystalofslope 1 n andµ= (1,0,...,0,0) isadominantcocharacterofGL n.IfXdenotestheFargues-Fontainecurve,

Fargues-Fontaine curve in nLab

WebJul 19, 2024 · The theory Fargues and Scholze developed provides exact mathematical directions for performing that gluing and certifies that, in the end, you will get the … WebThe goal of this text is to overview the Fargues–Fontaine curve, its role in p-adic Hodge theory, and its relation to Scholze’s theory of perfectoid spaces and diamonds. On the … snowy mountain nursery nc

Overview of Fargues–Scholze

WebJan 16, 2024 · Abstract. We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of \mathbf {C}_ {p}. It takes values in a mixed-characteristic analogue of Dieudonné modules, which was previously defined by Fargues as a version of Breuil–Kisin modules. Notably, this cohomology theory specializes to all … WebFargues–Scholze is to propose a uniform local Langlands correspondence, constructing a map π7→ϕ π, which comes out of some more powerful structure and which we hope … WebSep 2, 2024 · For and its inner forms, Fargues-Scholze and Hansen-Kaletha-Weinstein showed that the correspondence is compatible with the correspondence of Harris-Taylor/Henniart. We verify a similar compatibility for and its unique non-split inner form , where is the quaternion division algebra over , assuming that is unramified and . snowy mountain adk hike

(PDF) The Work of Peter Scholze Michael Rapoport - Academia.edu

Compatibility of the Fargues-Scholze and Gan-Takeda Local …

WebG-bundles. Recently, Fargues and Scholze constructed a general candidate for the local Langlands correspondence by doing geometric Langlands on the Fargues-Fontaine … WebJul 4, 2024 · This is another motivation for the appearance of the Fargues-Fontaine curve in the Fargues-Scholze geometrization of the local Langlands correspondence. Related concepts. p-adic Hodge theory. local Langlands correspondence. References. Jared Weinstein, The Fundamental Curve of p-adic Hodge Theory, or How to Un-tilt a Tilted Field snowy mountain 1 day tourWebMathematisches Institut der Universität Bonn snowy mountain minis

"WebL. Fargues and S. Scholze, Geometrization of the local langlands correspondence, arXiv:2102.13459, 2024. Erez Lapid and Zhengyu Mao, On the asymptotics of Whittaker functions, Represent. Theory 13 (2009), 63–81. MR 2495561, DOI 10.1090/S1088-4165-09 … " - Fargues-scholze

Fargues-scholze

Geometrization of the local Langlands correspondence

WebFeb 26, 2024 · We prove a generalization of the Jacobian criterion of Fargues-Scholze for spaces of sections of a smooth quasi-projective variety over the Fargues-Fontaine curve … WebIn geometric Langlands, you start with a curve X, and try to put into correspondence two very different-looking entities: Local systems of rank n on X on the one hand, and Hecke eigensheaves on Bun_n (X) on the other. In the recent work of Fargues-Scholze, there is a beautiful conjectural extension of this story to the p-adic setting.

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WebFargues-Scholze setting. In particular, we explain how, given the eigensheaf S_{\chi} on Bun_{T} attached to a smooth character \chi of the maximal torus T, one can construct an eigensheaf on Bun_{G} under a certain genericity hypothesis on \chi, by applying a geometric Eisenstein functor to S_{\chi}. Assuming the Fargues-Scholze WebTHE WORK OF PETER SCHOLZE M. RAPOPORT arXiv:1909.07222v1 [math.NT] 13 Sep 2024 Abstract. He has developed powerful methods in algebraic geometry over p-adic fields, and has proved striking theorems in this area. My purpose here is to convey some idea of the accomplishments of Peter Scholze for which he was awarded the Fields medal.

WebNov 7, 2024 · Since then, the main result of this article has been leveraged by other authors to complete parts of the Fargues-Scholze program. The geometry of shtuka spaces. The PI used his award to support the doctoral research of María Inés de Frutos Fernández, whose thesis provided us with the first explicit study of moduli spaces of shtukas over the ... WebFeb 11, 2024 · From another side of the geometric Langlands world, Peter Scholze is continuing his lectures on his ongoing work with Laurent Fargues that reformulates the local Langlands correspondence in terms of geometric Langlands on …

WebOct 20, 2024 · S=T for Shimura Varieties and Moduli Spaces of p-adic Shtukas. Zhiyou Wu. We prove the conjecture proposed by Xiao-Zhu in \cite {2024arXiv170705700X}, making use of Scholze's theory of diamonds and v-stacks and Fargues-Scholze's geometric Satake equivalence. We deduce the Eichler-Shimura relation for Shimura varieties of Hodge type. WebI’m heading out soon for a 10 day vacation in the Rocky Mountains, blogging likely to change from sparse to non-existent for the next couple weeks.

WebCompatibility of the Fargues-Scholze and Gan-Takeda Local Langlands The Fargues-Scholze LLC and compatibility for G= GLn Definition 1 Let µ∈X ∗(G Q p)+ be a …

WebJul 29, 2024 · The Fargues-Scholze work relates arithmetic and the central objects in geometric Langlands involving categories of bundles over curves. These categories in turn are related (in work of Witten and collaborators) to 4d TQFTs based on twistings of N=4 super Yang-Mills. This sort of 4d QFT involves much the same ingredients as 4d QFTs … snowy mountain fire towerWebPreprints/Publications. Geometric Eisenstein Series, Intertwining Operators, and Shin's Averaging Formula with an Appendix by Alexander Bertoloni-Meli () ; Compatibility of the Fargues-Scholze Correspondence for Unitary Groups Submitted with Alexander Bertoloni-Meli and Kieu-Hieu Nguyen () ; Compatibility of the Gan-Takeda and Fargues-Scholze … snowy mountain inn indian lakeWebApr 10, 2024 · Averaging functors in Fargues' program for GL_n. Johannes Anschütz, Arthur-César Le Bras. We study the so-called averaging functors from the geometric Langlands program in the setting of Fargues' program. This makes explicit certain cases of the spectral action which was recently introduced by Fargues-Scholze in the local … snowy mountain tree farmWebCOMPATIBILITY OF THE FARGUES–SCHOLZE CORRESPONDENCE FOR UNITARY GROUPS ALEXANDERBERTOLONIMELI,LINUSHAMANN,ANDKIEUHIEUNGUYEN … snowy mountain sceneryWeb1 French Land Register data, which excludes lakes, ponds, glaciers > 1 km 2 (0.386 sq mi or 247 acres) and river estuaries. Fargues ( French pronunciation: [faʁɡ]; Occitan: … snowy mountain resortsWebJun 2, 2024 · In the course of the Berkeley conference, Fargues worked out a reformulation of the above story using the Fargues-Fontaine curve, yielding his geometrization … snowy mountain range mapWebAs a consequence, we canonically lift Fargues–Scholze's construction to a non-semisimplified local Langlands correspondence for local fields of characteristic p ≥ 5. We also deduce that Fargues–Scholze's construction agrees with that of Genestier–Lafforgue, answering a question of Fargues–Scholze, Hansen, Harris, and Kaletha. The ... snowy mountain minecraft seed