On the Rationality of the Zeta Function of an Algebraic Variety
On the Rationality of the Zeta Function of an Algebraic Variety
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DOI：
10.2307/2372974
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发表时间：
1960-07
影响因子：
1.7
通讯作者：
B. Dwork
中科院分区：
文献类型：
--
作者：
B. Dwork
设p为素数，a2是有理p进数域的代数闭包，设A为Q的留数类域。域A是其素数子域的代数闭包，具有特征p。如果 T* 是 a2 中对 p 阶素数的所有单位根的集合，则残差类映射对 T* 的限制是 T* 在 R 乘法群上的乘法同构。T T* U {O} 的元素形成 Q2 中 A 的 Teichmiiller 表示，并且对于每个 x C A，Q 中 x 的表示将被理解为类 x 中 T 的元素。 0 的非阿基米德估值将由序数函数表示，缩写为“ord”，并通过条件 ord p = 1 进行标准化。
Let p be a prime number, a2 the completion of the algebraic closure of the field of rational p-adic numbers and let A be the residue class field of Q. The field A is the algebraic closure of its prime subfield and is of characteristic p. If T* is the set of all roots of unity in a2 of order prime to p then the restriction of the residue class map to T* is a multiplicative isomorphism of T* onto the multiplicative group of R. The elements of T T* U {O} form the Teichmiiller representatives of A in Q2 and for each x C A the representative of x in Q will be understood to be the element of T in the class x. The non-archimedean valuation of 0 will be denoted by the ordinal function, abbreviated "ord ", and normalized by the condition ord p = 1.