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Appendix a : Weil's Proof of Theorem 8. 1

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Book Id: WPLBN0000654339
Format Type: PDF eBook
File Size: 142.25 KB
Reproduction Date: 2005
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Title: Appendix a : Weil's Proof of Theorem 8. 1  
Language: English
Subject: Science., Mathematics, Logic
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Appendix a : Weil's Proof of Theorem 8. 1. (n.d.). Appendix a : Weil's Proof of Theorem 8. 1. Retrieved from

Mathematics document containing theorems and formulas.

Excerpt: Let P denote the set of all rational primes. For each p 2 P, the field of p{adic numbers, Qp, is defined to be the completion of the rationals in the p{adic valuation, jrjp = p ordp(r); where ordp(r) is the highest power of p dividing r. Extend the de nition of j jp by setting j0jp = 0. Write p = 1 for the usual valuation on Q, jrj1 = jrj. Then Q1 = R. For each p 2 f1g [ P, the field Qp is a non{discrete locally compact eld, with topology given by the metric dp(x; y) = jx yjp. For finite p, the metric is an ultrametric...


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