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Class groups of global function fields with certain splitting behaviors of the infinite prime

Title
Class groups of global function fields with certain splitting behaviors of the infinite prime
Authors
Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2009
Journal Title
Proceedings of the American Mathematical Society
ISSN
0002-9939JCR Link
Citation
vol. 137, no. 2, pp. 415 - 424
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
For certain two cases of splitting behaviors of the prime at infinity with unit rank r, given positive integers m,n, we construct infinitely many global function fields K such that the ideal class group of K of degree m over F(T) has n-rank at least m - r - 1 and the prime at infinity splits in K as given, where F denotes a finite field and T a transcendental element over F. In detail, for positive integers m, n and r with 0 ≤ r ≤ m - 1 and a given signature (ei,fi), 1 ≤ i ≤ r + 1, such that Σr+1i=1 eifi = m, in the following two cases where ei is arbitrary and fi = 1 for each i, or ei = 1 and fi's are the same for each i, we construct infinitely many global function fields K of degree m over F(T) such that the ideal class group of K contains a subgroup isomorphic to (ℤ/nℤ) m-r-1and the prime at infinity p;∞ splits into r + 1 primes β 1, β2, • • •, P r+1 in K with e(βi/p;∞) = e i and f(βi/p;infin;) = fi for 1 ≤ i ≤ r + 1 (so, K is of unit rank r). © 2008 American Mathematical Society.
DOI
10.1090/S0002-9939-08-09581-6
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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