But that's just for communication. What if one bank sends $100 to another bank without reducing their own reserve? The reserve is just numbers stored in computers stored locally at each bank, or is that information stored globally somewhere?
Banking is not as straightforward as one might think when reading these kind of discussions. The entire system is very complicated and regulated, and you just can't make "money out of thin air" or "just send money without reducing your reserve". The procedures are well documented and you just can't get in the industry by being a complete fraud.
My first language is not english so excuse me if I don't know all the right terms.
Banks need a banking permit in order to get in the business in the first place. These permits are given by the financial regulators in each country. One has to fulfill certain requirements in order to get the banking permit. One of the requirements is to have reliable systems in place. You don't do business with crappy and fraudulent software.
Now let me explain these systems a bit. You can't just type in an amount of your choosing without reducing any other account. They are built in a way, that a plus 1000 in one account is always a minus 1000 in some other account. So it a plus-minus-zero game. Normally, if you do transfers between customers, you take the money from one customer (-1000) and credit the other customer (+1000). If you just type in +1000 to some account, it doesn't mean that the money comes from nowhere. There are certain nominal ledger accounts (I looked the term in the dictionary, so I don't know if it's correct), that are debited in case no other debit account is given. And these nominal ledger accounts keep the record of your minuses.
So to put it simply, for every plus there is a minus somewhere else, and it is all being recorded. If you have no such systems in place, you are not getting a banking permit in the first place. The regulators do regular checks to and go through the finances and books of the banks, so you can't do bad business for long.
You are right in that SWIFT is for communication and messaging. It enables banks to do transactions easily and swiftly (I know). With SWIFT in place, the transactions are recorded and can be easily tracked (given a legal right to do so). For example, in the case of 9/11 attacks, SWIFT was used to track terrorist finances. That is to say, that everything is recorded and you just can't be a fraud in the business.