Unformatted text preview: .... iq)) (3.4.1.5) + ( 1) b I(D (io) D(ix))(og(il . .... iq)). Thus 17(D) is the sum of two terms. The first, of bidegree (0, 0), is the cupproduct with the 0chain {Lie(D(/))}. The second, of bidegree (1, 1), is the cupproduct with the 1cocycle I(D (i)D(j)). This explicit construction makes clear computationally the truth of (1.4.1.6), (1.4.1.7), and (2.3.0.1). In order to prove 3.2, it suffices by linearity to establish the com mutativity of the outermost square of (3.2.0), and after "contraction" with any D~Der(S/T). Thus we must prove commutative the diagram a b R f,(JY (f2~/s(logD))) r ~R,+lf,(gfb_l(f2~/s(logD))) (3.4.1.6) l~el~ l~eI ~ R"f,(ab/s(log O)) (1)b+10(D), RO+l f,(f~xSs~(log D)). Let us explicate the arrows in this diagram. The vertical ones are deduced from the morphisms of sheaves (3.4.1.7) f~bx/s (log D) "*, f~x,,,/s (log D ~"))~21 , o~ b (a}/s (log D))....
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 Fall '11
 NormanKatz
 Addition, Derivative, Algebraic Solutions of Differential Equations, chosen local coordinates

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