{"title":"Matthew Emerton","description":"\u003cp\u003eWelcome to our collection featuring the works of Matthew Emerton, an acclaimed scholar in the field of mathematics. Emerton is renowned for his contributions to number theory and the arithmetic aspects of algebraic geometry, where his research continues to influence contemporary thought. His insightful books, including \u003cem\u003eModuli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts\u003c\/em\u003e, delve into complex mathematical concepts with clarity and depth.\u003c\/p\u003e\n\n\u003cp\u003eThese works are perfect for those interested in exploring advanced topics within Science \u0026amp; Nature, providing educational resources for both budding mathematicians and seasoned experts alike. Emerton's writings offer a window into the intricate world of mathematical research, where theoretical frameworks and real-world applications intersect. As you explore his works, you're invited to engage with materials that are as fascinating as they are challenging.\u003c\/p\u003e\n\n\u003cp\u003eDiscover the intellectual rigor and the fascinating explorations in the mathematical sciences through Matthew Emerton's esteemed collection. Whether you are a student, researcher, or enthusiast, Emerton's works are a valuable addition to any collection in this domain.\u003c\/p\u003e","products":[{"product_id":"moduli-stacks-of-etale-ϕ-γ-modules-and-the-existence-of-crystalline-lifts-by-matthew-emerton-9780691241357","title":"Moduli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts","description":"\u003cdiv class=\"book-description\"\u003e\n\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\n\n\u003cp\u003eMotivated by the \u003ci\u003ep\u003c\/i\u003e-adic Langlands program, \u003ci\u003eModuli Stacks of Étale (ϕ, Γ)-Modules and the Existence of Crystalline Lifts\u003c\/i\u003e 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\u003e\u003csub\u003ep\u003c\/sub\u003e that parameterise étale (ϕ, Γ)-modules. The formal completions of these stacks at points in their special fibres recover the universal deformation rings of local Galois representations.\u003c\/p\u003e\n\n\u003cp\u003eThese 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-Mézard conjecture.\u003c\/p\u003e\n\n\u003cp\u003eAlong the way, it proves a number of foundational results in \u003ci\u003ep\u003c\/i\u003e-adic Hodge theory that may be of independent interest.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"NewSouth Books","offers":[{"title":"Default Title","offer_id":46854682083564,"sku":"9780691241357","price":160.0,"currency_code":"NZD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0705\/7784\/8556\/files\/e38480fa1a874c3fcd55dcb90942656e.jpg?v=1759266384"}],"url":"https:\/\/bookhero.co.nz\/collections\/matthew-emerton.oembed","provider":"Book Hero","version":"1.0","type":"link"}