DOI QR코드

DOI QR Code

ON HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS

  • Jung, Hwanyup (Department of Mathematics Education Chungbuk National University)
  • 투고 : 2010.07.07
  • 심사 : 2010.08.12
  • 발행 : 2010.09.30

초록

In this paper we prove that real quadratic function field F over ${\mathbb{F}}_q(T)$ has infinite 2-class field tower if the 4-rank of narrow ideal class group of F is equal to or greater than 4 when $q{\equiv}3$ mod 4.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea(NRF)

참고문헌

  1. S. Bae and H. Jung, l-rank of class groups of function fields. submitted for publication.
  2. H. Jung, Imaginary bicyclic function fields with the real cyclic subfield of class number one. Bull. Korean Math. Soc. 45 (2008), no. 2, 375-384. https://doi.org/10.4134/BKMS.2008.45.2.375
  3. F. Lemmermeyer, The 4-class group of real quadratic number fields. Preprint (1998).
  4. J. Martinet, Tours de corps de classes et estimations de discriminants. Invent. Math. 44 (1978), no. 1, 65-73. https://doi.org/10.1007/BF01389902
  5. M. Rosen, The Hilbert class field in function fields. Exposition. Math. 5 (1987), no. 4, 365-378.
  6. R. Schoof, Algebraic curves over $F_2$ with many rational points. J. Number Theory 41 (1992), no. 1, 6-14. https://doi.org/10.1016/0022-314X(92)90079-5