|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 Zp-extensions
Abstract: A Zp-extension 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 Zp-modules associated to each layer of the tower. Here, we will discuss some basic terminologies and facts about Zp-extensions 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 Zp-extensions obtained from adjoining p-th power roots of unity.
Speaker: Yifeng Huang