摘要翻译：
设k是一个可分离闭域。设K_i=[A_i\to B_i](i=1,2,3）是定义在K上的三个1-动机。定义了K_1的K_3扩张和(K_1,K_2)的K_3双扩张的几何概念。然后我们计算了这些新的几何概念的同调解释：即(K_1,K_2)的任意双扩张的自同构群biext^0(K_1,K_2；K_3)与上同调群ext^0(K_1×K_2,K_3)正则同构，而(K_1,K_2)的双扩张的同构类的群biext^1(K_1×K_2,K_3)与上同调群ext^1(K_1×K_2,K_3)正则同构。
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英文标题：
《Homological interpretation of extensions and biextensions of 1-motives》
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作者：
Cristiana Bertolin
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最新提交年份：
2012
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：K-Theory and Homology        K-理论与同调
分类描述：Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
代数和拓扑K-理论，与拓扑的关系，交换代数和算子代数
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英文摘要：
  Let k be a separably closed field. Let K_i=[A_i \to B_i] (for i=1,2,3) be three 1-motives defined over k. We define the geometrical notions of extension of K_1 by K_3 and of biextension of (K_1,K_2) by K_3. We then compute the homological interpretation of these new geometrical notions: namely, the group Biext^0(K_1,K_2;K_3) of automorphisms of any biextension of (K_1,K_2) by K_3 is canonically isomorphic to the cohomology group Ext^0(K_1 \otimes K_2,K_3), and the group Biext^1(K_1,K_2;K_3) of isomorphism classes of biextensions of (K_1,K_2) by K_3 is canonically isomorphic to the cohomology group Ext^1(K_1 \otimes K_2,K_3).
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PDF链接：
https://arxiv.org/pdf/0808.3267