dc.contributor.author | Saidi, M | |
dc.contributor.author | Tamagawa, A | |
dc.date.accessioned | 2018-10-15T09:41:10Z | |
dc.date.issued | 2018-10-30 | |
dc.description.abstract | We prove some new results on the arithmetic of abelian varieties over function fields of one variable over finitely generated (infinite) fields. Among other things, we introduce certain new natural objects `discrete Selmer groups' and `discrete Shafarevich-Tate groups', and prove that they are finitely generated $\Bbb Z$-modules. Further, we prove that in the isotrivial case, the discrete Shafarevich-Tate group vanishes and the discrete Selmer group coincides with the Mordell-Weil group. One of the key ingredients to prove these results is a new specialisation theorem \`a la N\'eron for first Galois cohomology groups, of the ($l$-adic) Tate module of abelian varieties which generalises N\'eron's specialisation theorem for rational points of abelian varieties. | en_GB |
dc.identifier.citation | Published online 30 October 2018. | en_GB |
dc.identifier.doi | 10.1515/crelle-2018-0024 | |
dc.identifier.uri | http://hdl.handle.net/10871/34297 | |
dc.language.iso | en | en_GB |
dc.publisher | De Gruyter | en_GB |
dc.rights.embargoreason | Under embargo until 30 October 2019 in compliance with publisher policy. | en_GB |
dc.rights | © De Gruyter 2018. | |
dc.title | On the arithmetic of abelian varieties | en_GB |
dc.type | Article | en_GB |
dc.identifier.issn | 0075-4102 | |
dc.description | This is the author accepted manuscript. The final version is available from De Gruyter via the DOI in this record. | en_GB |
dc.identifier.journal | Journal fur die Reine und Angewandte Mathematik | en_GB |