{"product_id":"mordell-weil-lattices-matthias-schtt-9789813293007","title":"Mordell-Weil Lattices","description":"\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book lays out the theory of Mordell-Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics.\u003c\/p\u003e The book presents all the ingredients entering into the theory of Mordell-Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell-Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of \u003ci\u003eE\u003c\/i\u003e\u003csub\u003e6\u003c\/sub\u003e, \u003ci\u003eE\u003c\/i\u003e\u003csub\u003e7\u003c\/sub\u003e and \u003ci\u003eE\u003c\/i\u003e\u003csub\u003e8\u003c\/sub\u003e. They also explain a connection to the classical topic of the 27 lines on a cubic surface.\u003cp\u003eTwo chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell-Weil lattices. Finally, the book turns to the rank problem-one of the key motivations for the introduction of Mordell-Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over \u003cb\u003eQ\u003c\/b\u003e and over \u003cb\u003eC\u003c\/b\u003e(\u003ci\u003et\u003c\/i\u003e) and work out applications to the sphere packing problem.\u003c\/p\u003e Throughout, the book includes many instructive examples illustrating the theory.\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Matthias Sch?t, Tetsuji Shioda\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 9813293004\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9789813293007\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/29\/2019\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 431\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.76lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 1.00d","brand":"Matthias Sch?t","offers":[{"title":"Hardcover","offer_id":44079708373247,"sku":"9789813293007","price":159.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_6dda32e0-de61-48d6-a837-414abcea7349.jpg?v=1685482683","url":"https:\/\/www.whiterainbookhouse.com\/products\/mordell-weil-lattices-matthias-schtt-9789813293007","provider":"WR Book House","version":"1.0","type":"link"}