If a nefarious miner tries to reward herself 10000 bitcoins after finding a correct PoW for her copy of the block, what is to prevent her from doing so ?

Is there some central place where the current correct reward is to be found so that everyone knows for certain what it is e.g. https://somewebsite.com/current_reward.xml ?

When a reward values changes, but not everyone hears about it, there are bound to be miners who submit valid PoW and blocks whose reward is out of sync with the larger consensus. How is that discrepancy dealt with?