Schumer wants to use a Senate motion to dismiss. It's unheard of; the Constitution requires a trial in the Senate.
Even before Schumer can make a motion to dismiss, the Senate must first choose someone to preside over the trial, most likely the President pro tempore Patty Murray (D-WA).
Then they have to adopt the rules for the trial, most likely the same rules that have been used in the prior impeachment trial. I don't think those rules included a motion to dismiss. The Senate rules for the Clinton impeachment trial included a motion to dismiss, but it wasn't used.
-PJ
Sadly, there is precedent for impeachment trails of non presidents to be presided over by the vice president. We could see Kamala Harris sitting as president of the senate. And the clown show will continue.