Re: [其他] 代數幾何
※ 引述《hau (小豪)》之銘言：
: 我讀 Hartshorne 的 Algebraic Geometry
: 作到 P.68 1.19 的(b)
: Let X be a topological space, let Z be a closed subset, U = X-Z
: j : U → X be its inclusion.
: (b) F be a sheaf on U. ( j_!(F) )_p is equal to F_p if p ∈ U,
: 0 if p is not belongs to U.
: 後面要證明 j_!(F) is the only sheaf on X which has this property.
: 唯一性這裡，我想到假設有另一個sheaf滿足這個性質，想證明它們是isomorphism
: 可是我定不出morphism，我覺得我根本想錯證法。
: 直覺上是對的，但這個要怎麼看？？~~
你漏了
j_!(\mathscr{F}) is the only sheaf on X which as this property,
and whose restriction to U is \mathscr{F}.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
最後這個 clause 很關鍵，拿來定 morphism
( j_!(F)(V) -> G(V) ) = { identity, V subseteq U
{ 0 , otherwise
然後 induce isomorphism on stalks.
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10/05 22:41, , 1F
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