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035   $a(DE-He213)978-3-540-44475-6
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100   $a20121227d2004      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aHeegner Modules and Elliptic Curves$b[electronic resource] /$fby Martin L. Brown
205   $a1st ed. 2004.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2004.
215   $a1 online resource (X, 518 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1849
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-22290-1 
327   $aPreface -- 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.
330   $aHeegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the cohomology of the Heegner module is the main technical result and is applied to prove the Tate conjecture for a class of elliptic surfaces over finite fields; this conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1849
606   $aNumber theory
606   $aAlgebraic geometry
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
606   $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019
615  0$aNumber theory.
615  0$aAlgebraic geometry.
615 14$aNumber Theory.
615 24$aAlgebraic Geometry.
676   $a512.3
700   $aBrown$b Martin L$4aut$4http://id.loc.gov/vocabulary/relators/aut$0108816
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996466476203316
996   $aHeegner modules and elliptic curves$9262236
997   $aUNISA