Let p be a prime number, and let k be an imaginary quadratic field in which p decomposes into two primes \mathfrak{ p} and \bar{ \mathfrak{ p}}. Let k_\infty be the unique Z_p-extension of k which is unramified outside of \mathfrak{ p}, and let K_\infty be a finite extension of k_\infty, abelian over k. Let U_\infty/C_\infty be the projective limit of principal semi-local units modulo elliptic units. We prove that the various modules of invariants and coinvariants of U_\infty/C_\infty are finite.
Categories: math.NT