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On torsors under elliptic curves and Serre's pro-algebraic structures
| hal.structure.identifier | Dipartimento di Matematica Pura e Applicata [Padova] | |
| dc.contributor.author | BERTAPELLE, Alessandra | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | TONG, Jilong | |
| dc.date.accessioned | 2024-04-04T03:21:53Z | |
| dc.date.available | 2024-04-04T03:21:53Z | |
| dc.date.created | 2013-11-21 | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 0025-5874 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194700 | |
| dc.description.abstractEn | Let $K$ be a local field with algebraically closed residue field and $X_K$ a torsor under an elliptic curve $J_K$ over $K$. Let $X$ be a proper minimal regular model of $X_K$ over the ring of integers of $K$ and $J$ the identity component of the Néron model of $J_K$. We study the canonical morphism $q\colon \mathrm{Pic}^{0}_{X/S}\to J$ which extends the biduality isomorphism on generic fibres. We show that $q$ is pro-algebraic in nature with a construction that recalls Serre's work on local class field theory. Furthermore we interpret our results in relation to Shafarevich's duality theory for torsors under abelian varieties. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | On torsors under elliptic curves and Serre's pro-algebraic structures | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00209-013-1247-5 | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.identifier.arxiv | 1204.2805 | |
| bordeaux.journal | Mathematische Zeitschrift | |
| bordeaux.page | 91-147 | |
| bordeaux.volume | 277 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1-2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01023394 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01023394v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematische%20Zeitschrift&rft.date=2014&rft.volume=277&rft.issue=1-2&rft.spage=91-147&rft.epage=91-147&rft.eissn=0025-5874&rft.issn=0025-5874&rft.au=BERTAPELLE,%20Alessandra&TONG,%20Jilong&rft.genre=article |
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