{"product_id":"moduli-stacks-of-tale-matthew-emerton-9780691241357","title":"Moduli Stacks of ﾉtale (\u0026#981;, \u0026#915;)-Modules and the Existence of Crystalline Lifts: (Ams-215)","description":"\u003cp\u003e\u003cb\u003eA foundational account of a new construction in the \u003ci\u003ep\u003c\/i\u003e-adic Langlands correspondence\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eMotivated by the \u003ci\u003ep\u003c\/i\u003e-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 \u003cb\u003eZ\u003c\/b\u003ep that parameterize 騁ale (ϕ, Γ)-modules; the formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations. These stacks are then used to show that all mod \u003ci\u003ep\u003c\/i\u003e representations of the absolute Galois group of a \u003ci\u003ep\u003c\/i\u003e-adic local field lift to characteristic zero, and indeed admit crystalline lifts. The book explicitly describes the irreducible components of the underlying reduced substacks and discusses the relationship between the geometry of these stacks and the Breuil-M騷ard conjecture. Along the way, it proves a number of foundational results in \u003ci\u003ep\u003c\/i\u003e-adic Hodge theory that may be of independent interest.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Matthew Emerton, Toby Gee\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 069124135X\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780691241357\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Princeton University Press\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/13\/2022\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 312\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.00lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.10h x 6.10w x 0.50d","brand":"Matthew Emerton","offers":[{"title":"Paperback","offer_id":44059488092415,"sku":"9780691241357","price":85.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_da4cd8ac-706b-4248-a07b-90b980cae4ee.jpg?v=1685058528","url":"https:\/\/www.whiterainbookhouse.com\/products\/moduli-stacks-of-tale-matthew-emerton-9780691241357","provider":"WR Book House","version":"1.0","type":"link"}