Involutory elliptic curves over 𝔽 q ( T )

Andreas Schweizer

Journal de théorie des nombres de Bordeaux (1998)

  • Volume: 10, Issue: 1, page 107-123
  • ISSN: 1246-7405

Abstract

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For n ∈ 𝔽 q [ T ] let G be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve X 0 ( 𝔫 ) . We determine all 𝔫 and G for which the quotient curve G ∖ X 0 ( 𝔫 ) is rational or elliptic.

How to cite

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Schweizer, Andreas. "Involutory elliptic curves over $\mathbb {F}_q(T)$." Journal de théorie des nombres de Bordeaux 10.1 (1998): 107-123. <http://eudml.org/doc/248173>.

@article{Schweizer1998,
abstract = {For $n \in \mathbb \{F\}_q [T]$ let $G$ be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve $X_0 (\mathfrak \{n\})$. We determine all $\mathfrak \{n\}$ and $G$ for which the quotient curve $G \setminus X_0 (\mathfrak \{n\})$ is rational or elliptic.},
author = {Schweizer, Andreas},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Drinfeld modular curve; involutory elliptic curves; genus},
language = {eng},
number = {1},
pages = {107-123},
publisher = {Université Bordeaux I},
title = {Involutory elliptic curves over $\mathbb \{F\}_q(T)$},
url = {http://eudml.org/doc/248173},
volume = {10},
year = {1998},
}

TY - JOUR
AU - Schweizer, Andreas
TI - Involutory elliptic curves over $\mathbb {F}_q(T)$
JO - Journal de théorie des nombres de Bordeaux
PY - 1998
PB - Université Bordeaux I
VL - 10
IS - 1
SP - 107
EP - 123
AB - For $n \in \mathbb {F}_q [T]$ let $G$ be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve $X_0 (\mathfrak {n})$. We determine all $\mathfrak {n}$ and $G$ for which the quotient curve $G \setminus X_0 (\mathfrak {n})$ is rational or elliptic.
LA - eng
KW - Drinfeld modular curve; involutory elliptic curves; genus
UR - http://eudml.org/doc/248173
ER -

References

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  1. [A&L] A.O. Atkin and J. Lehner, Hecke Operators on Γ0(m), Math. Annalen185 (1970), 134-160. Zbl0177.34901
  2. [Ge1] E.-U. Gekeler, Drinfeld-Moduln und modulare Formen über rationalen Funktionenkörpem, Bonner Mathematische Schriften119 (1980). Zbl0446.14018MR594434
  3. [Ge2] E.-U. Gekeler, Automorphe Formen über Fq (T) mit kleinem Führer, Abh. Math. Sem. Univ. Hamburg55 (1985), 111-146. Zbl0564.10026MR831522
  4. [Ge3] E.-U. Gekeler, Analytical Construction of Weil Curves over Function Fields, J. Théor. Nombres Bordeaux7 (1995), 27-49. Zbl0846.11037MR1413565
  5. [G&N] E.-U. Gekeler and U. Nonnengardt, Fundamental domains of some arithmetic groups over function fields, Internat. J. Math.6 (1995), 689-708. Zbl0858.11025MR1351161
  6. [G&R] E.-U. Gekeler and M. Reversat, Jacobians of Drinfeld Modular Curves, J. Reine Angew. Math.476 (1996), 27-93. Zbl0848.11029MR1401696
  7. [Ke] M. Kenku, A note on involutory Weil curves, Quat. J. Math. Oxford (Ser. 2) 27 (1976), 401-405. Zbl0355.14014MR437460
  8. [Kl] P.G. Kluit, On the normalizer of ro(N). Modular Functions of one Variable V, SpringerLNM601, BerlinHeidelbergNew York1977, 239-246. Zbl0355.10020MR480340
  9. [M&SD] B. Mazur and P. Swinnerton-Dyer, Arithmetic of Weil Curves, Invent. Math.25 (1974), 1-61. Zbl0281.14016MR354674
  10. [Sch1] A. Schweizer, Zur Arithmetik der Drinfeld'schen Modulkurven X0(n), Dissertation, Saarbrücken1996 
  11. [Sch2] A. Schweizer, Modular automorphisms of the Drinfeld modular curves X0(n), Collect. Math.48 (1997), 209-216. Zbl0865.11051MR1464024
  12. [Sch3] A. Schweizer, Hyperelliptic Drinfeld Modular Curves, in: Drinfeld modules, modular schemes and applications, Proceedings of a workshop at Alden Biesen, September 9-14, 1996, (E.-U. Gekeler, M. van der Put, M. Reversat, J. Van Geel, eds.), World Scientific, Singapore, 1997, pp. 330-343 Zbl0930.11039MR1630612

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