Can police take and go through your trashcans, just to look for evidence that will let them get a search warrant for drugs?

The U.S. Supreme Court has held that police do not need a warrant to search trash left for collection outside the perimeter of the home. The reasoning is that a person does not have a reasonable expectation of privacy in property he or she has abandoned or voluntarily turned over to third parties. Most state courts, including Arkansas, where you are from, have ruled the same way. By placing your trash at the curb, or anywhere outside the boundary line of your home, you have made it accessible to the public, and it loses its Fourth Amendment protection. So long as the police did not trespass on your property to reach your trash, anything they found in it is fair game and can be used to establish probable cause for a later search warrant. However, there may be other inadequacies of the search warrant, such as a lack of probable cause even considering whatever was found in the trash; knowing or recklessly made false statements in the affidavit submitted in support of the warrant; or failing to specify or appropriately limit the items to be seized during the search. On the other hand, not every invalid search warrant will result in the suppression of evidence. Courts will consider whether an invalid warrant nonetheless was issued "in good faith," and if so, the search can be upheld. I recommend you contact an experienced criminal defense lawyer in your jurisdiction who can review the search warrant in your case, and the surrounding facts and case law, and advise you as to your prospects of a successful challenge.