Chromatic Selmer groups and arithmetic invariants of elliptic curves

Florian Ito Sprung

doi:10.5802/jtnb.1190

Chromatic Selmer groups and arithmetic invariants of elliptic curves

Florian Ito Sprung

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes p. We sketch their role in establishing the p-primary part of the Birch–Swinnerton-Dyer formula in Sections 2–5, and then study the growth of the Mordell–Weil rank along the Z²p-extension of a quadratic imaginary number field in which p splits in Section 6.

Original language	English (US)
Pages (from-to)	1103-1114
Number of pages	12
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	33
Issue number	3.2
DOIs	https://doi.org/10.5802/jtnb.1190
State	Published - 2021

Keywords

Elliptic curves
Mordell–Weil rank
Selmer group

ASJC Scopus subject areas

Algebra and Number Theory

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10.5802/jtnb.1190

Cite this

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title = "Chromatic Selmer groups and arithmetic invariants of elliptic curves",

abstract = "Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes p. We sketch their role in establishing the p-primary part of the Birch–Swinnerton-Dyer formula in Sections 2–5, and then study the growth of the Mordell–Weil rank along the Z2p-extension of a quadratic imaginary number field in which p splits in Section 6.",

keywords = "Elliptic curves, Mordell–Weil rank, Selmer group",

author = "{Ito Sprung}, Florian",

note = "Funding Information: Manuscrit re{\c c}u le 12 d{\'e}cembre 2019, r{\'e}vis{\'e} le 9 juin 2020, accept{\'e} le 28 juillet 2020. Mathematics Subject Classification. 11G40, 11R23, 14H52. Mots-clefs. Elliptic curves, Selmer group, Mordell–Weil rank. Supported by Simons Collaboration Grant 635320 and NSF Grant DMS 2001280. Publisher Copyright: {\textcopyright} 2021, Institut de Mathematique de Bordeaux. All rights reserved.",

year = "2021",

doi = "10.5802/jtnb.1190",

language = "English (US)",

volume = "33",

pages = "1103--1114",

journal = "Journal de Theorie des Nombres de Bordeaux",

issn = "1246-7405",

publisher = "Universite de Bordeaux III (Michel de Montaigne)",

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T1 - Chromatic Selmer groups and arithmetic invariants of elliptic curves

AU - Ito Sprung, Florian

N1 - Funding Information: Manuscrit reçu le 12 décembre 2019, révisé le 9 juin 2020, accepté le 28 juillet 2020. Mathematics Subject Classification. 11G40, 11R23, 14H52. Mots-clefs. Elliptic curves, Selmer group, Mordell–Weil rank. Supported by Simons Collaboration Grant 635320 and NSF Grant DMS 2001280. Publisher Copyright: © 2021, Institut de Mathematique de Bordeaux. All rights reserved.

PY - 2021

Y1 - 2021

N2 - Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes p. We sketch their role in establishing the p-primary part of the Birch–Swinnerton-Dyer formula in Sections 2–5, and then study the growth of the Mordell–Weil rank along the Z2p-extension of a quadratic imaginary number field in which p splits in Section 6.

AB - Chromatic Selmer groups are modified Selmer groups with local information for supersingular primes p. We sketch their role in establishing the p-primary part of the Birch–Swinnerton-Dyer formula in Sections 2–5, and then study the growth of the Mordell–Weil rank along the Z2p-extension of a quadratic imaginary number field in which p splits in Section 6.

KW - Elliptic curves

KW - Mordell–Weil rank

KW - Selmer group

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JF - Journal de Theorie des Nombres de Bordeaux

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Chromatic Selmer groups and arithmetic invariants of elliptic curves

Abstract

Keywords

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