02947nam 22006255 450 99646647620331620200629203927.03-540-44475-010.1007/b98488(CKB)1000000000231355(SSID)ssj0000323738(PQKBManifestationID)11258081(PQKBTitleCode)TC0000323738(PQKBWorkID)10303912(PQKB)10570192(DE-He213)978-3-540-44475-6(MiAaPQ)EBC6284983(MiAaPQ)EBC5585016(Au-PeEL)EBL5585016(OCoLC)162128282(PPN)155180622(EXLCZ)99100000000023135520121227d2004 u| 0engurnn|008mamaatxtccrHeegner Modules and Elliptic Curves[electronic resource] /by Martin L. Brown1st ed. 2004.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2004.1 online resource (X, 518 p.) Lecture Notes in Mathematics,0075-8434 ;1849Bibliographic Level Mode of Issuance: Monograph3-540-22290-1 Preface -- Introduction -- Preliminaries -- Bruhat-Tits trees with complex multiplication -- Heegner sheaves -- The Heegner module -- Cohomology of the Heegner module -- Finiteness of the Tate-Shafarevich groups -- Appendix A.: Rigid analytic modular forms -- Appendix B.: Automorphic forms and elliptic curves over function fields -- References -- Index.Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the cohomology of the Heegner module is the main technical result and is applied to prove the Tate conjecture for a class of elliptic surfaces over finite fields; this conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.Lecture Notes in Mathematics,0075-8434 ;1849Number theoryAlgebraic geometryNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Number theory.Algebraic geometry.Number Theory.Algebraic Geometry.512.3Brown Martin Lauthttp://id.loc.gov/vocabulary/relators/aut108816MiAaPQMiAaPQMiAaPQBOOK996466476203316Heegner modules and elliptic curves262236UNISA