Invariants and coinvariants of semilocal units modulo elliptic units

Details Invariants and coinvariants of semilocal units modulo elliptic units Invariants and coinvariants of semilocal units modulo elliptic units

2011-02-23

arxiv.org/abs/1102.4705v2

Mathematics

Number Theory

13 pages

Scientific paper

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.

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