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vls/2603nrwcece.visuallibrary.netvdModuli stacks of étale (, )-modules and the existence of crystalline liftsModuli stacks of étale ([phi], [Gamma])-modules and the existence of crystalline liftsEmerton, MatthewautGee, TobyauttextbookLehrbuchPrincetonOxfordPrinceton University Press20232023monographicengix, 298 Seiten"Motivated by the p-adic Langlands program, this book constructs stacks that algebraize Mazur's formal deformation rings of local Galois representations. More precisely, it constructs Noetherian formal algebraic stacks over Spf Zp that parameterize étale ([phi], [Gamma])-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. Matthew Emerton and Toby Gee use these stacks to show that all mod p representations of the absolute Galois group of a p-adic local field lift to characteristic zero, and indeed admit crystalline lifts. They explicitly describe the irreducible components of the underlying reduced substacks and discuss the relationship between the geometry of these stacks and the Breuil-Mézard conjecture. Along the way, they prove a number of foundational results in p-adic Hodge theory that may be of independent interest"--Matthew Emerton, Toby GeeIncludes bibliographical references and indexAlgebraic stacksModuli theoryGeometry, AlgebraicMATHEMATICSGeometryAlgebraicMATHEMATICSReference|QA564KXP1815037768978-0-691-24134-0978-0-691-24135-7HT021706089Annals of mathematics studiesnumber 215HT001233128Moduli stacks of étale ([phi], [Gamma])-modules and the existence of crystalline liftsEmerton, MatthewOnline-Ausgabe978-0-691-24136-4466TEG596220230127202303142513889rda https://ce.visuallibrary.net//domainresource/static/graphics/connectors/viewerLogo.gif http://193.30.112.129:83/F/?func=find-c&ccl_term=ICS%3D2513889 https://ce.visuallibrary.net/id/1180075 https://ce.visuallibrary.net/i3f/v20/1180075/manifest https://ce.visuallibrary.net/proto_ftsearch/1180075