{"product_id":"berkeley-lectures-on-p-adic-geometry-9780691202082","title":"Berkeley Lectures on P-Adic Geometry","description":"\u003cp\u003e • Author(s): Peter Scholze\u003cbr\u003e • Publisher: Princeton University Press\u003cbr\u003e • Publisher Imprint: Princeton University Press\u003cbr\u003e • BISAC: Geometry - Algebraic\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eBerkeley Lectures on p-adic Geometry\u003c\/i\u003e presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of \u003ci\u003ep\u003c\/i\u003e-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of \"diamonds,\" which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a \u003ci\u003ep\u003c\/i\u003e-adic field. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eThis book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores \u003ci\u003ep-\u003c\/i\u003eadic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including \u003ci\u003ep\u003c\/i\u003e-divisible groups, \u003ci\u003ep\u003c\/i\u003e-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. \u003ci\u003eBerkeley Lectures on p-adic Geometry\u003c\/i\u003e will be a useful resource for students and scholars working in arithmetic geometry and number theory.","brand":"Princeton University Press","offers":[{"title":"Paperback","offer_id":45082525859991,"sku":"9780691202082","price":10083.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780691202082.webp?v=1769200958","url":"https:\/\/atlanticbooks.com\/products\/berkeley-lectures-on-p-adic-geometry-9780691202082","provider":"Atlantic Books","version":"1.0","type":"link"}