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Input: By Jake HortonBBC Reality Check His lawyers filed a 78-page brief setting out their defence, and both sides have been presenting their arguments during the trial. We've fact-checked some of the claims. Claim: A Senate trial is unconstitutional The Senate has voted on this issue and decided that the trial of a former president is constitutional - but Mr Trump's lawyers argue that because he is no longer the president, a trial in Senate isn't permitted. The Democrats say they are able to finish off what they started before he left office. This point has caused some legal debate, because the US constitution doesn't explicitly lay out a course of action under these circumstances. However, the prevailing legal view is that if an impeachment begins when an individual is in office (as Mr Trump was), the process may continue after they depart. The Congressional Research Service reported that "most scholars who have closely examined the question have concluded that Congress has authority to extend the impeachment process to officials who are no longer in office". Until now, there has been no case of a president being tried in the Senate after leaving office, although other government officials have been. In 1876, the House impeached President Ulysses S Grant's war secretary, William Belknap, even after he resigned from his post. The Senate considered whether it still had jurisdiction to hear the case of a former official, and determined that it did. Claim: Mr Trump did not encourage violence from supporters The Democrats say: "It was clear that President Trump was comfortable urging, approving, and even celebrating violence." Mr Trump's lawyers deny this, claiming that the president "did not direct anyone to commit unlawful actions". During his speech before the riot, the president said: "I know that everyone here will soon be marching over to the Capitol building to peacefully and patriotically make your voices heard." This is the only time he mentioned the word "peacefully". In contrast he used the word "fight" 14 times, although he never explicitly directed his supporters to enter the Capitol building. His lawyers say the rhetoric was in regards to the need to fight for more election security. It's also important to note that protesters were already planning on marching to the US Capitol, and some were heading that way before Mr Trump finished speaking. The Democrats point to further examples of the president encouraging violence in the months leading up to the riot. For example, in the first presidential debate, Mr Trump told the Proud Boys, a violent far-right group, to "stand back and stand by". He also denounced violence on several other occasions, including condemning the Proud Boys and other far-right groups following the first of the presidential debates. Claim: Mr Trump did not act swiftly to stop the riot US media reported that Mr Trump initially resisted sending in reinforcements to the Capitol, and his vice-president, Mike Pence, ultimately approved the deployment of the National Guard. The Democrats say this represents a "dereliction of duty", citing the press reports which are yet to be confirmed publicly by Mr Pence or anyone else from within Mr Trump's cabinet. Defense Department officials say that the Capitol Police did not request additional help from National Guard troops prior to the riot. Mr Trump's former chief of staff, Mark Meadows, has also pushed back on this assertion, saying the president "literally at the very first said we need to make sure they have the resources". About two-and-a-half hours after Mr Trump's speech ended, the White House Press Secretary Kayleigh McEnany tweeted: "At President Donald Trump's direction, the National Guard is on the way along with other federal protective services." Claim: Mr Trump has the right to express his opinion Democrats say Mr Trump presented his supporters with a series of false claims about the election result in the build-up to the Capitol riot. Mr Trump's lawyers argue he has the the right to express his opinion on the election result and other matters - pointing to the first amendment of the US constitution which protects freedom of speech. A letter signed by 144 constitutional lawyers argues that this protection could apply as a defence in legal proceedings, but not to an impeachment trial. These lawyers say that the Senate is determining whether to convict Mr Trump based on the president violating his oath of office, rather than if he acted illegally. Mr Trump's lawyers have also said there is "insufficient evidence" to disprove there was widespread election fraud, although this isn't expected to feature as an argument during the Senate trial. The allegations of fraud have been rejected by the courts, with more than 50 legal challenges to the election results failing to provide adequate evidence. Claim: Mr Trump was denied due process Mr Trump's lawyers say his impeachment in the House of Representatives was unfair as its speed denied him due process. The US Constitution says an individual cannot be "deprived of life, liberty, or property" without "due process of law". But constitutional experts say this right doesn't apply to impeachment proceedings, as depriving the president of power doesn't require the same protection. During Mr Trump's first impeachment, proceedings in the House lasted more than two weeks, and witnesses were called to testify. That didn't happen this time round, with proceedings lasting just two days. Democrat impeachment manager, Ted Lieu, says "the House had a good reason to move quickly" and this was not "a case where there was hidden conduct or some conspiracy that required months or years of investigating". What claims do you want BBC Reality Check to investigate? Get in touch Read more from Reality Check

Trump impeachment: Fact-checking the Senate trial