Yes fresh Serrano peppers can be frozen to extend their life.
If you have more hot peppers or more fresh Serrano peppers than you can reasonably eat within a short time to prevent them from getting spoiled then freezing the peppers would be a good option to make them last longer.
I've always just placed the hot peppers including the fresh Serrano peppers inside a freezer safe bag to help keep them fresh while frozen.
You can also refrigerate them to make them last a bit longer than keeping them at room temperature but freezing the fresh Serrano peppers will make them last for a year or more.
Freezing makes foods including hot peppers and other peppers such as fresh Serrano peppers last longer than they would at room temperature.