LEADER 04678nam 22007695 450 001 9910349327203321 005 20200704093440.0 010 $a981-329-301-2 024 7 $a10.1007/978-981-32-9301-4 035 $a(CKB)4100000009606215 035 $a(MiAaPQ)EBC5946207 035 $a(DE-He213)978-981-32-9301-4 035 $a(PPN)258059435 035 $a(EXLCZ)994100000009606215 100 $a20191017d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMordell?Weil Lattices /$fby Matthias Schütt, Tetsuji Shioda 205 $a1st ed. 2019. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2019. 215 $a1 online resource (436 pages) 225 1 $aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v70 311 $a981-329-300-4 327 $aIntroduction -- Lattices -- Elliptic Curves -- Algebraic surfaces -- Elliptic surfaces -- Mordell--Weil Lattices -- Rational Elliptic Surfaces -- Rational elliptic surfaces and E8-hierarchy -- Galois Representations and Algebraic Equations -- Elliptic K3 surfaces. 330 $aThis book lays out the theory of Mordell?Weil lattices, a very powerful and influential tool at the crossroads of algebraic geometry and number theory, which offers many fruitful connections to other areas of mathematics. The book presents all the ingredients entering into the theory of Mordell?Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After defining Mordell?Weil lattices, the authors provide several applications in depth. They start with the classification of rational elliptic surfaces. Then a useful connection with Galois representations is discussed. By developing the notion of excellent families, the authors are able to design many Galois representations with given Galois groups such as the Weyl groups of E6, E7 and E8. They also explain a connection to the classical topic of the 27 lines on a cubic surface. Two chapters deal with elliptic K3 surfaces, a pulsating area of recent research activity which highlights many central properties of Mordell?Weil lattices. Finally, the book turns to the rank problem?one of the key motivations for the introduction of Mordell?Weil lattices. The authors present the state of the art of the rank problem for elliptic curves both over Q and over C(t) and work out applications to the sphere packing problem. Throughout, the book includes many instructive examples illustrating the theory. 410 0$aErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics,$x0071-1136 ;$v70 606 $aAlgebraic geometry 606 $aCommutative algebra 606 $aCommutative rings 606 $aAlgebra 606 $aField theory (Physics) 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aNonassociative rings 606 $aRings (Algebra) 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 606 $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 606 $aNon-associative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11116 615 0$aAlgebraic geometry. 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 0$aAlgebra. 615 0$aField theory (Physics). 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 0$aNonassociative rings. 615 0$aRings (Algebra). 615 14$aAlgebraic Geometry. 615 24$aCommutative Rings and Algebras. 615 24$aField Theory and Polynomials. 615 24$aCategory Theory, Homological Algebra. 615 24$aNon-associative Rings and Algebras. 676 $a511.33 700 $aSchütt$b Matthias$4aut$4http://id.loc.gov/vocabulary/relators/aut$0782093 702 $aShioda$b Tetsuji$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349327203321 996 $aMordell?Weil Lattices$92508242 997 $aUNINA