Splitting of Iwasawa Modules and Leopoldt Conjecture

Splitting of Iwasawa Modules and Leopoldt Conjecture - Jean-Pierre Wintenberger

Jean-Pierre Wintenberger
University of Strasbourg
October 20, 2010

Let p be an odd prime number and let F be a totally real field. Let F_cyc be the cyclotomic extension of F generated by the roots of unity of order a power of p . From the maximal abelian extension of F_cyc which is unramified (resp. unramified outside auxiliary primes), we get exact sequences of Iwasawa modules. We will discuss how splitting of these exact sequences are linked to Leopoldt conjecture for F and p . (JW with C. Khare)