Let p be an odd prime and F∞ a p-adic Lie extension of a number field F with Galois group G. Suppose that G is a compact pro-p p-adic Lie group with no torsion and that it contains a closed normal subgroup H such tha...Let p be an odd prime and F∞ a p-adic Lie extension of a number field F with Galois group G. Suppose that G is a compact pro-p p-adic Lie group with no torsion and that it contains a closed normal subgroup H such that G/H≌Zp. Under various assumptions, we establish asymptotic upper bounds for the growth of p-exponents of the class groups in the said p-adic Lie extension. Our results generalize a previous result of Lei, where he established such an estimate under the assumption that H≌Zp.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11550110172 and 11771164)
文摘Let p be an odd prime and F∞ a p-adic Lie extension of a number field F with Galois group G. Suppose that G is a compact pro-p p-adic Lie group with no torsion and that it contains a closed normal subgroup H such that G/H≌Zp. Under various assumptions, we establish asymptotic upper bounds for the growth of p-exponents of the class groups in the said p-adic Lie extension. Our results generalize a previous result of Lei, where he established such an estimate under the assumption that H≌Zp.
