Units from 3- and 4-torsion on jacobians of curves of genus 2

David Grant

Compositio Mathematica (1994)

  • Volume: 94, Issue: 3, page 311-320
  • ISSN: 0010-437X

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Grant, David. "Units from 3- and 4-torsion on jacobians of curves of genus 2." Compositio Mathematica 94.3 (1994): 311-320. <http://eudml.org/doc/90339>.

@article{Grant1994,
author = {Grant, David},
journal = {Compositio Mathematica},
keywords = {torsion; curve of genus 2; number field; Jacobian; units},
language = {eng},
number = {3},
pages = {311-320},
publisher = {Kluwer Academic Publishers},
title = {Units from 3- and 4-torsion on jacobians of curves of genus 2},
url = {http://eudml.org/doc/90339},
volume = {94},
year = {1994},
}

TY - JOUR
AU - Grant, David
TI - Units from 3- and 4-torsion on jacobians of curves of genus 2
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 94
IS - 3
SP - 311
EP - 320
LA - eng
KW - torsion; curve of genus 2; number field; Jacobian; units
UR - http://eudml.org/doc/90339
ER -

References

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  1. [B-K] W.L. Baily and M.L. Karel, appendix to: W.L. Baily, Reciprocity laws for special values of Hilbert modular functions, in Algebra and Topology (1986) 62-139, Korea Inst. Tech., Taejon, 1987. MR957926
  2. [Bo] J. Boxall: Valeurs spéciales de fonctions abéliennes, Groupe d'Etude sur les Problémes Diophantiens 1990-91, Publications Mathématiques de l'Université Pierre et Marie Curie No. 103. 
  3. [BaBo] E. Bavencoffe and J. Boxall: Valeurs des fonctions thêta associées a la courbe y2 = x5 - 1, Séminaire de Théories des Nombres de Caen 1991/2. 
  4. [BoBa] J. Boxall and E. Bavencoffe: Quelques propriétés arithmétiques des points de 3-division de la jacobienne de y2 = x5 - 1, Séminaire de Théories des Nombres, Bordeaux4 (1992) 113-128. Zbl0766.14019MR1183921
  5. [CW] J. Coates and A. Wiles: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39 (1977) 223-251. Zbl0359.14009MR463176
  6. [deS] E. de Shalit: Iwasawa Theory of Elliptic Curves with Complex Multiplication. Perspectives in Mathematics3, Academic Press, Orlando, 1987. Zbl0674.12004MR917944
  7. [F] A. Fröhlich: Formal Groups, Lecture Notes in Math. 74, Springer-Verlag, Berlin, 1968. Zbl0177.04801MR242837
  8. [G1] D. Grant: Formal groups in genus two, J. reine. angew. Math.411 (1990) 96-121. Zbl0702.14025MR1072975
  9. [G2] D. Grant: On a generalization of a formula of Eisenstein, Proc. London Math. Soc.3 (1991) 121-132. Zbl0738.14019MR1078216
  10. [G3] D. Grant: Some product formulas for genus 2 theta functions, preprint. 
  11. [I] J.-I. Igusa: Arithmetic variety of moduli for genus two, Ann. Math.72(3) (1960) 612-649. Zbl0122.39002MR114819
  12. [K] V.A. Kolyvagin: Euler systems, in The Grothendieck Festschrift II, Prog. Math.87 (1990) 435-483. Zbl0742.14017MR1106906
  13. [M] D. Mumford:Tata Lectures on Theta II.Prog. Math.43 (Birkhäuser, Boston) 1984. Zbl0549.14014MR742776
  14. [Ro] G. Robert: Unités elliptiques, Bull. Soc. Math. France. Mémoire36 (1973). Zbl0314.12006MR469889
  15. [Ru1] K. Rubin: Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Invent. Math.89 (1987) 527-560. Zbl0628.14018MR903383
  16. [Ru2] K. Rubin: The "main conjectures" of Iwasawa theory for imaginary quadratic fields, Invent. Math.103 (1991) 25-68. Zbl0737.11030MR1079839
  17. [S] H. Stark: L-functions at s = 1. IV. First derivatives at s = 0, Adv. Math.35(3) (1980) 197-235. Zbl0475.12018MR563924

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