《Galois cohomology》 J.P.S. p.73 * * * 13:30 Corollary . Let n be an integer ≥ 1, p rime to the characteristic of k. ---- 令 n 为自然数，并且与 k 的特征互质. ---- 基本域 k 的特征是什么 ? . Let μ n be the group of n-th roots of unity (in k s ). ---- ...
《Galois cohomology》 J.P.S. p.73 * * * 11:10 1.2 First examples . Let G a (resp. G m ) be the additive (resp. multiplicative) group, defined by the relation G a (K) = K (resp. G m (K) = K*). We have (cf. , p. 158): ---- 设 G a 为加法群，由关系 G a( K) = K 定义 ...
《Galois cohomology》 J.P.S. p.72 * * * 12:20 In particular, we see that two seperable closures of k define cohomology groups H^q(ks/k, A) which correspond bijectively and canonically to each other. ---- k 的两个可分闭包定义上同调群 H^q(ks/k, A)，它们彼此双射、规范地对应. . ...
《Galois cohomology》 少一点思考就多一点效率 ~ * * * 9:50 Let K' 1 /K 1 and K' 2 /K 2 be two Galois extensions, with Galois groups G 1 and G 2 . ---- 取两个 Galois 扩展，及对应的 Galois 群. . &nbs ...
《Galois cohomology》 适当地放慢速度 ~ * * * 16:20 Let A be a functor verifying the above axioms. ---- 令 A 为函子且符合三条公理. . 评论：此处直接从函子出发. . If K'/K is a Galois extension, the H^q(Gal(K'/K), A(K')) are defined. ---- 若 K'/K ...
《Galois cohomology》 在“待定”学习法中学习者不必理解每个知识点，正如在代数运算中允许存在未知元那样. * * * 15:20 Remarks. 1) If k s denotes a separable closure of k, the group A(k s ) is well-defined, and it is a Gal(k s /k)-group. ---- 若 ks 是 k ...
《Galois cohomology》 * * * 16:50 ... and this functor verifies the following axioms: ---- 这一函子符合如下公理: . 评论：这里所说的函子就是 A(K). . (1) A(K) = lim A(K i ), for K i running over the set of sub-extensions of K of finite type over k. - ...
《Galois cohomology》 * * * 11:50 In fact, it is often more convenient not to work with a fixed extension K/k. ---- K/k 不固定更好. . The situation is the following: ---- 情况是这样的. . One has a ground field k, and a functo r K ~ A(K) defined on the category of ...
要抓住大写字母... * * * 9:10 Let k be a field, and let K be a Galois extension of k. ---- 设立一个域和它的 Galois 扩域. ---- 域和扩域都是集合 (后者包含前者). . The Galois group Gal(K/k) of the extension K/k is a profinite group (cf. Chap.I.S1.1)... ---- K/k 是扩张，以它为基础得到 ...
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