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摘要翻译：
关于场$F$的$K$-理论有两个无限小（即加法）版本：一个是由凯瑟琳诺提出的，它是一个$F$-模，另一个是由布洛赫-埃斯诺提出的，它是一个$F^*$-模。当$F$是复数字段时，这两个版本都配备了调节器映射。在我们的简短论文中，我们将介绍一个扩展的Cathelineau群，以及一个由熵给出的复值调节器映射。我们还将给出我们的扩展版本和凯瑟琳诺的小组之间的对比图。我们的结果是由两个无关的来源推动的：Neumann关于扩展Bloch群的工作（它同构于复数的不可分解的$K_3$)和生成超几何多和级数的奇点的研究。最终版本。
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英文标题：
《An extended version of additive K-theory》
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作者：
Stavros Garoufalidis
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最新提交年份：
2007
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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：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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英文摘要：
There are two infinitesimal (i.e., additive) versions of the $K$-theory of a field $F$: one was introduced by Cathelineau, which is an $F$-module, and another one introduced by Bloch-Esnault, which is an $F^*$-module. Both versions are equipped with a regulator map, when $F$ is the field of complex numbers. In our short paper we will introduce an extended version of Cathelineau's group, and a complex-valued regulator map given by the entropy. We will also give a comparison map between our extended version and Cathelineau's group. Our results were motivated by two unrelated sources: Neumann's work on the extended Bloch group (which is isomorphic to indecomposable $K_3$ of the complex numbers), and the study of singularities of generating series of hypergeometric multisums. Final version.
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PDF链接：
https://arxiv.org/pdf/0707.1828
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