Most of the information I can gleen about the extradition treaty between Chile & Peru comes in articles about the extradition of Fujimori which began in 2005 although it looks like he wasn't actually extradited until 2007. But he was a prominent political figure and his situaiton was a bit different then VDS. The Extradition Treaty is from 1932 and I can't find one in English.
An article on the Living in Peru website
http://www.livinginperu.com/news/offers the best description I've found and reinforces what I read about needing a Peruvian rather than an Interpol wrarrant to begin extradition.
If he has committed any infraction against Chilean migratory laws, he could be promptly expelled and deported to Peru, after some administrative paperwork, said on air attorney Roberto Miranda, one of the professionals consulted by Radio Capital. But if there is no violation to any Chilean law, then we would need Chile to extradite him to Peru to face trial here, and that would mean another legal procedure.
Peruvian Justice would need to issue today an arrest warrant on Joran van der Sloot, signed by a judge, before being able to take any legal action, warned Miranda.
Chilean police, however, estimate it is likely van der Sloot may be expelled and sent to Peru."
And, one of his fellow countrymen doesn't think Dutch authorities will intervene on his behalf and that he will have to serve his sentence in a Peruvian jail as there is no judicial treaty between the two countries!
"In addition, odds are that Netherlands will not intervene in favor of its citizen, in opinion of Dutch law professor Geert-Jan Knoops.
I assume that Joran is the main suspect in the Peru murder case and that the Peruvian authorities will want to prosecute him. In that case, he is an ordinary suspect. All the Netherlands can do is give him consular assistance," he told Dutch media.
If van der Sloot is convicted in Peru, he will have to serve his sentence in Peru, since there is no judicial treaty between Peru and the Netherlands that may allow him to serve his sentence in a Dutch jail.
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