Date: Wednesday, March 21, 2018
Location: 1866 East Hall (3:00 PM to 4:00 PM)
Title: Introduction to Iwasawa theory  Weak Leopoldt conjecture for cyclotomic Zpextensions
Abstract: A Zpextension of a number field is an extension whose Galois group is isomorphic to Zp, and it naturally gives rise to a tower of Z/p^n extensions of number fields. Iwasawa theory originally studies the ideal class groups of the fields in such a tower, via the study of certain Galois groups that have natural Zp[[T]]module structures. The weak Leopoldt conjecture is a statement about the asymptotic behavior of some Galois Zpmodules associated to each layer of the tower. Here, we will discuss some basic terminologies and facts about Zpextensions and Zp[[T]]modules to understand the statement of weak Leopoldt conjecture. If time permits, we will discuss the idea from Kummer theory to verify this conjecture for Zpextensions obtained from adjoining pth power roots of unity.
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Speaker: Yifeng Huang
Institution: UM
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