题目：The simplicity of the (class group) of the p-cyclotomic field

报告人：Professor Preda Mihailescu

摘要：: In this lecture we shall derive three consequences from the truth of the KummerVandiver Conjecture. Let K ’= Q[ζp] and K = K’+; let A0 = (C(K))p. Let K’∞ be the Zp-cyclotomic extension of K0’and H∞ be its maximal p-abelian unramified extension; let X = Gal(H/K’∞). We prove

1. The exponent of A is p.

2. The exponent of the maximal p-abelian p-ramified extension of K, that intersects K∞ in K,is also p – this is equivalent to Kummer’s condition that units of K that are local p2-powers must also be global p-powers.

3. The spectral components of X are Zp-cyclic or trivial.

Let L/K be a p-ramified cyclic real extension of degree p, which is also galois over Q. Such extensions exist for irregular primes p. The results are deduced using an extensive investigation of the Iwasawa complex of L: Units and local units in the cyclotomic Zp-extension, p-class groups and maximal pabelian p-ramified extensions, etc. The first two facts complete together with the Kummer-Vandiver conjecture a Kummerian proof of FLT.

报告时间：2024年10月10日（周四）下午15:00-17:00

报告地点：教二楼727

联系人：杜少飞