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warrant of arrest
The general way to express this idea in English, which I often come across with in various texts, is to simply use the word “warrant” (this word alone can stand for “order na arest”), or to modify it, in order to be more specific. Examples are “a search warrant” (order na obysk) and, what you are looking for in this instance, “arrest warrant” (I verified “arrest warrant”, using ABBYY Lingvo 6.0 dictionary and search engines). Another way to put it is “warrant of arrest”.
In your context, you can use any of the three (“warrant”, “arrest warrant” or “warrant of arrest”). This will translate the idea completely. I would translate the segment of your sentence into English as follows:
Based on the arrest warrant, which was issued by the judge of N district of Moscow on 15 July 1999, …
There is quite a number of other English words for “order na arest”. Below are some of the examples (more context-specific than the general ones, which I recommend above, and which I encourage you to use in your context) that I found in my bilingual dictionaries.
mittimus I n
юр. приказ о заключении в тюрьму; ордер на арест
mittimus II v юр.
заключать в тюрьму на основании ордера на арест или распоряжения суда
ордер на арест (= writ of capias)
ордер на арест
letters of caption — ордер на арест
to serve a warrant on smb. — предъявлять кому-л. ордер на арест
Hope that this will be helpful.
Electronic dictionaries and web search
artyan United States Local time: 18:18 Native speaker of: Russian PRO pts in pair: 134