L-Functions and Tamagawa Numbers of Motives
L-Functions and Tamagawa Numbers of Motives
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DOI：
10.1007/978-0-8176-4574-8_9
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
S. Bloch;Kazuya Kato
中科院分区：
文献类型：
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作者：
S. Bloch;Kazuya Kato
母题的概念最早是由A. Grothendieck，本文试图了解他的一些想法的算术的影响。我们将提出一个关于与动机相关的L-函数在整数点处的值的猜想。猜想由于德利涅和贝林森表示这些价值观“moduloQ* 倍数”在阿基米德周期或监管积分。我们的目的是通过定义实际上是什么多摩川数的动机来消除Q * 的模糊性。基本的技术工具，这是Fontaine-Messing理论的p-adic上同调。作为我们的玉川数猜想的证据，我们表明，它是兼容的isketos，我们包括强大的结果，由于我们之一（加藤）的黎曼zeta函数和椭圆曲线与复杂的乘法。
The notion of a motif was first defined and studied by A. Grothendieck, and this paper is an attempt to understand some of the implications of his ideas for arithmetic. We will formulate a conjecture on the values at integer points of L-functions associated to motives. Conjectures due to Deligne and Beilinson express these values “moduloQ* multiples” in terms of archimedean period or regulator integrals. Our aim is to remove theQ* ambiguity by defining what are in fact Tamagawa numbers for motives. The essential technical tool for this is the Fontaine-Messing theory ofp-adic cohomology. As evidence for our Tamagawa number conjecture, we show that it is compatible with isogeny, and we include strong results due to one of us (Kato) for the Riemann zeta function and for elliptic curves with complex multiplication.