The police can come and arrest you at your home. However, under the 4th amendment, there are rights to protect individuals from searches, seizures, and unlawful arrests.
Firstly, it is important to understand the difference between seizures and unlawful arrests. A seizure happens when government agents create a situation where a reasonable person will not feel free to leave an encounter with an agent.
An arrest happens when a policeman takes a person into custody, against their will. This is done usually for purposes of interrogation or criminal prosecution. All arrests in order to be lawful need to adhere to the probable cause requirement. This means that the arrest should be on grounds that there is sufficient knowledge based on trustworthy facts that suggests that the suspect has committed the crime. Law enforcement officials do not need the warrant to arrest someone. However, they will require a warrant to arrest someone in non-emergency situations.
If an official enters your home, they are required to knock and announce their identity, before forcible entry. If this process is not adhered to and an arrest has been made, it can be later found to be unlawful. However, in the case of suspects dealing with drugs, police do not have to follow this procedure. If there are occupants in the home or premises, these occupants can also be detained.