If an arrest warrant is issued does that mean a statement was made under oath? If so if a part of the statement for the arrest warrant is proven false what are the implications? In the case of a search warrant that would mean that an argument for removing any evidence obtained under the search warrant but what does it mean if a person is arrested to be charged but part of the justification was in fact incorrect. more than a clerical error but a statement of existing evidence showing something it clearly doesn't. For example the statement says there is evidence this person was at the place at the time of the crime but the actual evidence puts the person there weeks after the crime and not at the time of the crime.
To get a warrant, there must be an affidavit. Here is an example of such affidavits, also here, and here. Some general guidance on preparation of the affidavit is here, which says you must "Swear to the contents of the affidavit and sign it before the judge/magistrate" (as we observe in the examples).
If a part of the statement for the arrest warrant is proven false, then the question would arise as to whether the person sweating knew that it was false. If he knew it was false, that constitutes perjury, which is a crime (and could invalidate the warrant, thus the evidence). If he is simply mistaken, that is not a crime, and does not invalidate the warrant.
A statement that there is evidence this person was at the place at the time of the crime is not sufficient to yield a warrant, and would not be perjury (it is a conclusion based on fact: perjury pertains to statements of fact, not conclusions drawn from facts). The statement would need to say how it is known that the person was there. If the statement is that "two eyewitnesses saw him" and that is just a lie, that is perjury. If the eyewitnesses change their minds about who they saw, or if it is later found that the eyewitnesses were lying, reporting that is not a wrongful act by the officer.
The affidavit must be "fully truthful", and may not omit material facts. Suppose that two people claim to have seen the accused at the scene but the officer has credible evidence that they are lying, then the report must include that information (a Washington case here, a California case here).