Justice Elena Kagan asks Michael Dreeben what should be done about all the "lingering issues" that go beyond the breadth of what is charged in this case, but are mentioned in Donald Trump's immunity claims.

Dreeben replies that the court has the discretion to rule on the case but that some questions were not raised by the Trump team in their previous appeals.

He also alleges that the former president is "smuggling in other issues" within its appeal.

"We would want to guide the court not to have an expansive approach to that issue," Dreeben adds, saying existing laws affirm the nature of the government's prosecution.

Image source, Getty Images

Anthony Zurcher
BBC North America correspondent

Two justices, Brett Kavanaugh and Samuel Alito, have expressed concern about the fraud statute the special counsel’s office is relying on in its indictment of Donald Trump for allegedly attempting to overturn the 2020 presidential election results.

The court is also considering the legality of 6 January prosecutions, using a law that prohibits the obstruction of official proceeding - another statute that is central to Trump’s criminal charges.

The fraud statute is not a central issue of this case, but today’s oral arguments could be an indication that if Trump were ultimately convicted for violating that statute, there are at least two justices on the Supreme Court who might have doubts about the validity of the verdict.

And if the court rules later this year that the obstruction law has also been wrongly applied, the case against Trump could be on very shaky ground.

Justice Sotomayor steps in after that long back-and-forth with Alito, who asked if US democracy could be at risk without presidential immunity.

Sotomayor responds with something of a speech.

There is no fail-safe system of justice, she says. "We fail routinely, but we succeed more often than not".

"In the end, if it fails completely, it's because we've destroyed our democracy on our own, isn't it?"

Alito still has the floor with Dreeben, as they continue to debate the government's argument.

Alito asks "if the president gets advice from the attorney general that something is lawful, is that an absolute defence" for the actions they take?

"Yes I think it is," Dreeben replies. "If an authorised government representative tells you what you are about to do is lawful, it would be a violation of due process to prosecute you."

Alito asks whether that then provides a president the incentive to pick a 'yes man' as their attorney general.

Dreeben notes that presidents can only nominate the attorney general candidate and the Senate must provide advice and consent to confirm that nominee.

"These are the sort of structural checks that have operated for 200 years to prevent the kind of abuses that [Trump's lawyer] fears going forward as a result of this once-in-history prosecution," he says.

The conservative justices have been hitting Michael Dreeben with some sharp questions this morning, and Justice Alito is no exception.

He grills Dreeben on whether the president would be subject to prosecutions in the same way any other US citizen would.

"Did I understand you to say... if [the president] makes a mistake... He's subject to the criminal laws just like anybody else?"

"You don't think he's in a special, peculiarly precarious position?" he questions.

Dreeben responds and says that "making a mistake" is not what lands you under criminal prosecution.

The US Supreme Court doesn't allow cameras in the courtroom when it's in session, but you can listen to proceedings by clicking the Play button at the top of this page.

We'll also have live text updates of the opening arguments right here. Stay tuned.

Oral arguments are typically a dense affair - and this session has been no different.

We keep hearing the justices use the word tautological over and over again.

It means that the same thing is being said twice, in different ways. Simple, everyday examples are "prepay in advance" or "honest truth".

What the justices are doing here is picking apart the US Court of Appeals for the DC Circuit's decision earlier this year against Donald Trump's immunity argument, as they try to determine what questions might yet need to be answered.

Image source, Alex Wong via Getty

Justice Brett Kavanaugh comes in with a very different hypothetical scenario.

He gives the example of a president staging a peaceful protest outside Congress, which could be seen as impeding an official proceeding. That's a crime we've seen some of the people from the 6 January attack accused of committing.

Dreeben says, "probably not", when asked if the president could be prosecuted after leaving office in this instance.

Anthony Zurcher
BBC North America correspondent

If the Supreme Court expressed scepticism toward Donald Trump’s claims of blanket presidential immunity, they also seem reluctant to endorse the prosecution’s assertion that presidents are open to criminal prosecution even for clearly official actions.

Chief Justice John Roberts wondered whether the lower court should have made a more detailed review of the facts of Trump’s case before “taking away immunity”. He expressed concern – which has been hammered by Trump’s defence team – that failing to grant former president’s some form of immunity might open them up to bad faith prosecutions.

Michael Dreeben, arguing for the prosecution, said he was not endorsing a rule that would allow prosecutions involving “bad faith, political animus, without adequate evidence".

Several court justices don’t seem so sure.

Image source, Alex Wong via Getty

Justice Samuel Alito, nominated by Republican President George W Bush, raises some of the problems with prosecuting a former president.

It could keep them from campaigning, Alito says, and if there is a trial, it would come at great expense of time and money, preventing that person from doing other things he or she wants to do.

Alito's comments may hold extra meaning today, as former President Trump, in the midst of his election campaign, will be in New York for several weeks as his criminal trial there unfolds.

You can follow our live coverage of that trial here.

You might notice that we keep hearing about the "framers" - these are the people who drafted the constitution of the United States back in the late 1700s, often known as the Founding Fathers - George Washington, Thomas Jefferson, Alexander Hamilton and Benjamin Franklin were among them.

We're hearing a lot about Franklin, who was also a leading writer, scientist and philosopher.

Lawyers and justices are talking about the framers as they try to get to the meaning of different parts of the constitution on presidents. They're especially looking at Article 2, which lays out the duties of the president and how one could be impeached and removed from office.

Image source, Getty Images

Chief Justice John Roberts proposes to Michael Dreeben that the court may have to issue an opinion that takes into account whether prosecutors are acting in good or bad faith.

He asks whether the government is arguing "a former president can be prosecuted because he is being prosecuted".

Dreeben disputes this claim, saying that the case clearly invokes federal criminal law and the indictment of Donald Trump came after the allegations were presented to a grand jury.

Roberts pushes back, noting that it is "easy" for prosecutors to build a case that receives a greenlight from a grand jury. He adds this happens "in some cases - I'm not suggesting that's the case here".

So, he asks, "why shouldn't we either send it back to the Court of Appeals or issue an opinion making clear that's not the law?"

Dreeben says there are "layered safeguards" to protect against unconstitutional and politically-driven prosecutions.

"We are not endorsing a regime that we think would expose former presidents to criminal prosecution in bad faith, for political animus, without adequate evidence."

Clarence Thomas, the longest-serving Supreme Court Justice, kicks off the questions again, as per usual.

He asks: If there isn't blanket presidential immunity for official acts, how have there never been prosecutions of presidents before?

Thomas references "various coups" through history, including "Operation Mongoose", the CIA's attempt to remove Fidel Castro from power in Cuba.

Dreeben responds that there have been no prosecutions "because there were not crimes". There are "layers of safeguards" in place to protect presidents from criminal liability for doing their job, including actions taken overseas.

Before Dreeben started speaking, Justice Ketanji Brown Jackson said the Oval Office risks becoming a "seat of criminal activity" which allows the president to commit "crime with abandon".

She raised concern about a president having those kinds of powers, "the most powerful person in the world with the greatest amount of authority", going into office knowing that there would be no potential penalty for committing crimes.

"I'm trying to understand what the disincentive is from turning the Oval Office into the seat of criminal activity in this country," she said.

Trump's lawyer, Sauer, responded that he doesn't think there's any allegation of that in Trump's case.

She then asked: if the potential of criminal liability is taken off table, wouldn't there would be a significant risk that future presidents would be emboldened to commit crimes with abandon while they're in office?

Phew. That was an intense hour of questioning for Donald Trump's lawyer, Dean John Sauer.

Now we're hearing from his opponent - Michael Dreeben, a long-time Justice Department official.

"This court has never recognised absolute criminal immunity for any public official," he begins.

But Trump is claiming that he has "permanent criminal immunity for his official acts unless he was first impeached and convicted".

"His novel theory would immunise former presidents for criminal liability for bribery, treason, sedition, murder - and here, conspiring to use fraud to overturn the results of an election and perpetuate himself in power."

This argument "has no foundation in the constitution" and would make Trump akin to "a king who could do no wrong".

Under questions from Justice Amy Coney Barrett, Sauer turns to another one of Trump's arguments: that a president needs to be impeached by Congress, before they can be criminally prosecuted for that same act.

"You admit that if the president was successfully impeached, he could be convicted," says Justice Barrett, a Trump appointee. "But you also say that these criminal statutes don’t apply to him."

So, Barrett continues, how can you be subject to prosecution if the criminal statutes do not apply?

Barrett also asks why other US officers subject to impeachment - a group that includes all nine of the Supreme Court Justices - are not also protected from criminal prosecution.

Image source, Reuters/ Jane Rosenberg

Yep. That’s a different one, happening in New York (this one is at the Supreme Court in Washington DC).

In Manhattan, Donald Trump is sitting in a criminal trial - the first ever for a US president, current or former - where he is accused of falsifying his business records to hide hush-money payments to adult film star, Stormy Daniels. He denies any wrongdoing.

You can follow the BBC’s live coverage of that trial here.

About 45 minutes in, Justice Brett Kavanaugh has a question for Trump's lawyer - and he is the first jurist this morning to express sympathy for his arguments.

He affirms that the legal statutes under which Donald Trump is charged do not clearly apply to the office of president. Sauer agrees that they "extend way beyond" what the law suggests.

"And then just to clarify this - that the president's not above the law, the president's not a king... I think your point in response to that is the president is subject to prosecution for all personal acts just like every other American?" he asks.

Sauer reiterates a core argument - that presidents are subject to criminal prosecution if Congress impeaches and convicts them, in addition to "a whole series of [other] structural checks" that would deter them from improper actions.

As a reminder, Trump was twice impeached in the House of Representatives but acquitted both times by the Senate.

Kavanaugh, who was appointed by Trump, also helps Sauer bolster his point that the founding fathers claimed that executive immunity must be expressly taken away from a president's actions.

"That's absolutely correct," Sauer responds. "It would have to be expressly taken away."

Image source, Getty Images

Justice Gorsuch is bringing up presidential pardons.

He asks Trump's lawyer: "What would happen if presidents were under fear that their successors would criminally prosecute them for their acts in office?" He lists hypothetical examples such as if they were engaged in a drone strike.

He adds: "It seems to me like one of the incentives that might be created, is for presidents to try to pardon themselves."

Sauer replies: "That is certainly one incentive that might be created. The real concern is, is there going to be bold and fearless action?

"Is the president going to make decisions where his political opponents are going to come after him as soon as he leaves office?"

Justice Elena Kagan is digging in on the main subject so far today: what is an official act?

She presents another hypothetical to Sauer: what if the president orders the military to stage a coup, is that an official act?

Sauer responds that it would "depend on the circumstances whether it was an official act".

Kagan, a liberal justice, sounds incredulous in her response: "That sounds pretty bad, doesn't it?"

Image source, Getty Images