On Jacquet-Langlands isogeny over function fields

Mihran Papikian

doi:10.1016/j.jnt.2011.01.002

On Jacquet-Langlands isogeny over function fields

Mihran Papikian

Mathematics

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

7 Scopus citations

Abstract

We propose a conjectural explicit isogeny from the Jacobians of hyperelliptic Drinfeld modular curves to the Jacobians of hyperelliptic modular curves of D-elliptic sheaves. The kernel of the isogeny is a subgroup of the cuspidal divisor group constructed by examining the canonical maps from the cuspidal divisor group into the component groups.

Original language	English (US)
Pages (from-to)	1149-1175
Number of pages	27
Journal	Journal of Number Theory
Volume	131
Issue number	7
DOIs	https://doi.org/10.1016/j.jnt.2011.01.002
State	Published - Jul 2011

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jnt.2011.01.002

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title = "On Jacquet-Langlands isogeny over function fields",

abstract = "We propose a conjectural explicit isogeny from the Jacobians of hyperelliptic Drinfeld modular curves to the Jacobians of hyperelliptic modular curves of D-elliptic sheaves. The kernel of the isogeny is a subgroup of the cuspidal divisor group constructed by examining the canonical maps from the cuspidal divisor group into the component groups.",

author = "Mihran Papikian",

note = "Funding Information: 1 The author was supported in part by NSF grant DMS-0801208.",

year = "2011",

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doi = "10.1016/j.jnt.2011.01.002",

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Y1 - 2011/7

N2 - We propose a conjectural explicit isogeny from the Jacobians of hyperelliptic Drinfeld modular curves to the Jacobians of hyperelliptic modular curves of D-elliptic sheaves. The kernel of the isogeny is a subgroup of the cuspidal divisor group constructed by examining the canonical maps from the cuspidal divisor group into the component groups.

AB - We propose a conjectural explicit isogeny from the Jacobians of hyperelliptic Drinfeld modular curves to the Jacobians of hyperelliptic modular curves of D-elliptic sheaves. The kernel of the isogeny is a subgroup of the cuspidal divisor group constructed by examining the canonical maps from the cuspidal divisor group into the component groups.

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M3 - Article

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EP - 1175

JO - Journal of Number Theory

JF - Journal of Number Theory

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ER -

On Jacquet-Langlands isogeny over function fields

Abstract

All Science Journal Classification (ASJC) codes

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