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As an analogy of $Poincar{\acute{e}}$ series in the space of modular forms, T. Ono associated a module $M_c/P_c$ for ${\gamma}=[c]{\in}H^1(G,R^{\times})$ where finite group G is acting on a ring R. $M_c/P_c$ is regarded as the 0-dimensional twisted Tate cohomology ${\hat{H}}^0(G,R^+)_{\gamma}$. In the case that G is the Galois group of a Galois extension K of a number field k and R is the ring of integers of K, the vanishing properties of $M_c/P_c$ are related to the ramification of K/k. We generalize this to arbitrary n-dimensional twisted cohomology of the ring of integers and obtain the extended version of theorems. Moreover, some explicit examples on quadratic and biquadratic number fields are given.
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참고문헌 (11)
참고문헌 신청
A. Babakhanian / 1972 / Cohomological Methods in Group Theory / Marcel Dekker, INC
E.K. Lee / 2005 / On Certain Cohomological Invariants of Algebraic Number Fieds
M.P. Lee / 1969 / On the Galois cohomology of the ring of integers in an algebraic number eld / Proc. Amer. Soc 20(2):405~408
S.M. Lee / 2003 / On a certain invariant for real quadratic elds / Proc. Japan Acad. Ser. A 79(8):119~122
T. Ono / 2003 / A Note on Poincar e sums for nite groups / Proc. Japan Acad. Ser. A 79(4):95~97
E.K. Lee / 2005 / On Certain Cohomological Invariants of Algebraic Number Fieds
M.P. Lee / 1969 / On the Galois cohomology of the ring of integers in an algebraic number eld / Proc. Amer. Soc 20(2):405~408
S.M. Lee / 2003 / On a certain invariant for real quadratic elds / Proc. Japan Acad. Ser. A 79(8):119~122
T. Ono / 2003 / A Note on Poincar e sums for nite groups / Proc. Japan Acad. Ser. A 79(4):95~97
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