Decompositions of an Abelian surface and quadratic forms

Shouhei Ma[1]

  • [1] University of Tokyo Graduate School of Mathematical Sciences 3-8-1 Komaba, Meguro-ku Tokyo 153-8914 (Japan)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 2, page 717-743
  • ISSN: 0373-0956

Abstract

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When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.

How to cite

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Ma, Shouhei. "Decompositions of an Abelian surface and quadratic forms." Annales de l’institut Fourier 61.2 (2011): 717-743. <http://eudml.org/doc/219812>.

@article{Ma2011,
abstract = {When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.},
affiliation = {University of Tokyo Graduate School of Mathematical Sciences 3-8-1 Komaba, Meguro-ku Tokyo 153-8914 (Japan)},
author = {Ma, Shouhei},
journal = {Annales de l’institut Fourier},
keywords = {Abelian surface; elliptic curve; binary quadratic form; abelian surface; isogeny},
language = {eng},
number = {2},
pages = {717-743},
publisher = {Association des Annales de l’institut Fourier},
title = {Decompositions of an Abelian surface and quadratic forms},
url = {http://eudml.org/doc/219812},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Ma, Shouhei
TI - Decompositions of an Abelian surface and quadratic forms
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 2
SP - 717
EP - 743
AB - When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.
LA - eng
KW - Abelian surface; elliptic curve; binary quadratic form; abelian surface; isogeny
UR - http://eudml.org/doc/219812
ER -

References

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  13. T. Shioda, N. Mitani, Singular abelian surfaces and binary quadratic forms, Classification of algebraic varieties and compact complex manifolds 412 (1974), 259-287, Springer Zbl0302.14011MR382289
  14. H. M. Stark, On complex quadratic fields with class-number two, Math. Comp. 29 (1975), 289-302 Zbl0321.12009MR369313
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