Étale $K$-theory and arithmetic
Étale $K$-theory and arithmetic
复制标题
Étale $K$-理论和算术
DOI：
10.1090/s0273-0979-1982-15013-3
复制
发表时间：
1982
影响因子：
1.3
通讯作者：
E. Friedlander
中科院分区：
文献类型：
--
作者：
W. Dwyer;E. Friedlander
请注意。如果K是完全虚数，则可以去掉/是奇素数的要求。(1.1)右边的群是连续的/-进的上同调群。回想一下，Z//(L)表示单位根的^次根，Z/P(I)=(Z//(L))？，Z，(0=HMV Z/L(I))。D.Quillen曾猜想(1.1)型同构的存在。B.Harris和G.Segal[4]证明了：当k=1时，(1.1)是扭满射；C.Soule[6]在许多情况下用i<；i证明了k=2时的满射性。(1.1)的满射性与A.Borel对K^(0)®Q[1]的计算一起给出了同构存在的新的证明[7]。
REMARK . The requirement that / be an odd prime can be dropped if K is totally imaginary. The groups on the right of (1.1) are continuous /-adic etale cohomology groups. Recall that Z//(l) denotes the sheaf of ^th roots of unity, Z/P(i) = (Z//(l))®, and Z,(0 = Hmv Z/l (i). D. Quillen has conjectured the existence of isomorphisms of type (1.1). B. Harris and G. Segal [4] have shown that (1.1) is surjective on torsion if k = 1; C. Soule [6] in many cases proved surjectivity for k = 2 with i < I. The surjectivity of (1.1) together with A. Borel's computation of K^(0) ® Q [1] gives a new proof of the existence [7] of isomorphisms