J ul 2 00 8 On fake Z p - extensions of number fields
نویسنده
چکیده
For an odd prime number p, let Fanti be the Zp-anticyclotomic extension of an imaginary quadratic field F . We focus on the non-normal subextension K∞ of Fanti fixed by a subgroup of order 2 in Gal(Fanti/Q). After providing a general result for dihedral extensions, we study the growth of the p-part of the class group of the subfields ofK∞/Q, providing a formula of Iwasawa type. Furthermore, we describe the structure of the projective limit of these class groups.
منابع مشابه
0 M ay 2 00 9 On fake Z p - extensions of number fields
For an odd prime number p, let L∞ be the Zp-anticyclotomic extension of an imaginary quadratic field L. We focus on the non-normal subextension K∞ of L∞ fixed by a subgroup of order 2 in Gal(L∞/Q). After providing a general result for dihedral extensions, we study the growth of the p-part of the class group of the subfields of K∞/Q, providing a formula of Iwasawa type. Furthermore, we describe ...
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