Federal courts have SMJ over matters involving litigants who are citizens of different states, countries, IF the amount in controversy is more than $75K. If the defendant can prove "to a legal certainty" that the plaintiff's claim does not exceed $75K, the action will be dismissed for lack of SMJ.
*a green card holder living in VA and a VA citizen are NOT diverse
*There must be COMPLETE diversity. If any defendant is from the same state as any plaintiff, there is no longer diversity (except for class action lawsuits with over 100 people and $5 million in controversy, which requires only minimal diversity)
*Diversity must exist at time of filing
*Domicile requires some form of physical presence (e.g. living there or owning property there) + intent to live there indefinitely. E.g. if a resident of Virginia takes a longterm work assignment in Maryland but still owns a house in VA and intends to remain in VA indefinitely, he is still domiciled in VA.
*a corporation is a citizen of BOTH where it is incorporated, and where it has its principal place of business ("nerve center" where executives coordinate the activities). If it shares any one of these with another, there is no diversity
*In cases of estate planning, probate, divorce, child custody, and family law, federal courts decline jurisdiction and defer to state courts (even if there is complete diversity)