The isomorphism between Lubin-Tate and Drinfeld towers

zbMath1136.14001MaRDI QIDQ880213

Laurent Fargues, Alain Genestier, Vincent Lafforgue

Publication date: 14 May 2007

Published in: Progress in Mathematics (Search for Journal in Brave)

zbMATH Keywords

moduli spacelocal Langlands correspondenceLubin-Tate toweretale cohomologyformal groupDrinfeld towerrigid spaceformal schemeperiod spaceRapoport-Zink-space

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) (p)-adic theory, local fields (11F85) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Modular and Shimura varieties (14G35) Rigid analytic geometry (14G22) Formal groups, (p)-divisible groups (14L05) Langlands-Weil conjectures, nonabelian class field theory (11R39) Class field theory; (p)-adic formal groups (11S31)

Related Items

The Kudla-Rapoport conjecture at a ramified prime for 𝑈(1,1), \(\mathcal{O}\)-displays and \(\pi\)-divisible formal \(\mathcal{O}\)-modules, Harder-Narasimhan strata and 𝑝-adic period domains, On the p-adic cohomology of the Lubin-Tate tower, Differential operators and families of automorphic forms on unitary groups of arbitrary signature, Semistable models for modular curves of arbitrary level, Monodromy of perverse sheaves on vanishing cycles on some Shimura varieties, Drinfeld symmetric space and local Langlands correspondence. II, Breuil 𝒪-windows and 𝜋-divisible 𝒪-modules, Good reduction of affinoids in the Lubin-Tate curve in even equal characteristic. I., Rigid analytic \(p\)-divisible groups. II, A PEL case of the Kottwitz conjecture, On torsion in the cohomology of locally symmetric varieties, Rigid analytix \(p\)-divisible groups, Galois irreducibility implies cohomology freeness for KHT Shimura varieties, The Kottwitz conjecture for unitary PEL-type Rapoport-Zink spaces, Special cycles on the basic locus of unitary Shimura varieties at ramified primes, Locally analytic representations in the étale coverings of the Lubin-Tate moduli space, STABLE MODELS OF LUBIN–TATE CURVES WITH LEVEL THREE, Overconvergent modular sheaves and modular forms for \(\mathrm{GL}_{2/F}\), Cell decomposition of some unitary group Rapoport-Zink spaces, PARITY OF THE LANGLANDS PARAMETERS OF CONJUGATE SELF-DUAL REPRESENTATIONS OF AND THE LOCAL JACQUET–LANGLANDS CORRESPONDENCE, \(p\)-divisible groups with Pappas-Rapoport condition and Hasse invariants, Note on weight-monodromy conjecture for $p$-adically uniformized varieties, Symmetric Drinfeld space and local Langlands correspondence. I, Nonabelian Lubin-Tate theory and elliptic representations, Overconvergent modular forms and perfectoid Shimura curves, Structured ring spectra and displays, Filtrations de stratification de quelques variétés de Shimura simples, Lubin-Tate and Drinfeld bundles, Cohomologie 𝑝-adique de la tour de Drinfeld: le cas de la dimension 1, Shtukas adiques, modifications et applications, Abelian surfaces over totally real fields are potentially modular, Good reduction of affinoids in the Lubin-Tate curve in even equal characteristic. II, Perfectoid Drinfeld modular forms, The canonical filtration of \(p\)-divisible \({{\mathcal{O}}}\)-modules, Le lemme fondamental métaplectique de Jacquet et Mao en égales caractéristiques, \(l\)-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients