TY - JOUR
T1 - The 2-primary class group of certain hyperelliptic curves
AU - Cornelissen, Gunther
N1 - Funding Information:
The author is post-d octoral fellow of the Fund for Scientific Research - Fland ers (FWO - Vlaanderen). This work was done while visiting the MPIM.
PY - 2001/11
Y1 - 2001/11
N2 - Let q be an odd prime, e a non-square in the finite field Fq with q elements, p(T) an irreducible polynomial in Fq[T] and A the affine coordinate ring of the hyperelliptic curve y2 = ep(T) in the (y, T)-plane. We use class field theory to study the dependence on deg(p) of the divisibility by 2, 4, and 8 of the class number of the Dedekind ring A. Applications to Jacobians and type numbers of certain quaternion algebras are given.
AB - Let q be an odd prime, e a non-square in the finite field Fq with q elements, p(T) an irreducible polynomial in Fq[T] and A the affine coordinate ring of the hyperelliptic curve y2 = ep(T) in the (y, T)-plane. We use class field theory to study the dependence on deg(p) of the divisibility by 2, 4, and 8 of the class number of the Dedekind ring A. Applications to Jacobians and type numbers of certain quaternion algebras are given.
UR - http://www.scopus.com/inward/record.url?scp=0035215008&partnerID=8YFLogxK
U2 - 10.1006/jnth.2001.2680
DO - 10.1006/jnth.2001.2680
M3 - Article
AN - SCOPUS:0035215008
SN - 0022-314X
VL - 91
SP - 174
EP - 185
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -