TY - JOUR
T1 - Rumely's local global principle for algebraic psc fields over rings
AU - Jarden, Moshe
AU - Razon, Aharon
N1 - Funding Information:
ACKNOWLEDGMENTS. Cryo-EM micrographs were collected at the David Van Andel Advanced Cryo-Electron Microscopy Suite at the Van Andel Research Institute. We thank Drs. Gongpu Zhao and Xing Meng for facilitating data collection. We are also grateful to Dr. Olga Yurieva (Rockefeller University) for WT Pol δ and Pol δexo- and to Dr. Nina Yao (Rockefeller University) for the Pol31-Pol32 complex. This work was supported by the NIH (GM131754, to H.L. and GM115809, to M.E.O.) and the Howard Hughes Medical Institute (M.E.O).
PY - 1998
Y1 - 1998
N2 - Let S be a finite set of rational primes. We denote the maximal Galois extension of Q in which all p ε S totally decompose by N. We also denote the fixed field in N of e elements σ1,... ,εe in the absolute Galois group G(Q) of Q by N(σ). We denote the ring of integers of a given algebraic extension M of Q by ZM. We also denote the set of all valuations of M (resp., which lie over S) by VM/ (resp., SM)- If ε VM then OM, denotes the ring of integers of a Henselization of A/ with respect to v. We prove that for almost all σ ε G(Q)e, the field M = N(cr) satisfies the following local global principle: Let V be an affine absolutely irreducible variety defined over M. Suppose that V(OM,v) ≠ Ø for each v ε VM\SM and Vsim(OM,v) ≠ Ø for each v ε SM. Then V(OM) ≠ Ø. We also prove two approximation theorems for M.
AB - Let S be a finite set of rational primes. We denote the maximal Galois extension of Q in which all p ε S totally decompose by N. We also denote the fixed field in N of e elements σ1,... ,εe in the absolute Galois group G(Q) of Q by N(σ). We denote the ring of integers of a given algebraic extension M of Q by ZM. We also denote the set of all valuations of M (resp., which lie over S) by VM/ (resp., SM)- If ε VM then OM, denotes the ring of integers of a Henselization of A/ with respect to v. We prove that for almost all σ ε G(Q)e, the field M = N(cr) satisfies the following local global principle: Let V be an affine absolutely irreducible variety defined over M. Suppose that V(OM,v) ≠ Ø for each v ε VM\SM and Vsim(OM,v) ≠ Ø for each v ε SM. Then V(OM) ≠ Ø. We also prove two approximation theorems for M.
KW - Absolute galois group
KW - Field of totally 5-adic numbers
KW - Global fields
KW - Haar measure
KW - Henselian fields
KW - Local global principle
KW - P5c fields over rings
KW - Pac field over rings
KW - Valuations
UR - http://www.scopus.com/inward/record.url?scp=21944444792&partnerID=8YFLogxK
U2 - 10.1090/s0002-9947-98-01630-4
DO - 10.1090/s0002-9947-98-01630-4
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AN - SCOPUS:21944444792
VL - 350
SP - 55
EP - 85
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 1
ER -