WASHINGTON — One of the country’s top lawyers is asking the Supreme Court to take up a case that could reshape — or even end — the death penalty in America.

The aggressive filing comes as the Supreme Court is already set to hear a high-profile series of cases.

An Arizona death row inmate, Abel Daniel Hidalgo, has been arguing for the past three years that the state’s death penalty law is unconstitutional because it doesn’t do enough to narrow who is eligible for the death penalty among those convicted of murder.

Earlier this year, Neal Katyal, best known these days for serving as the lead lawyer for Hawaii’s challenge to President Trump’s travel ban, agreed to serve as Hidalgo’s lawyer at the Supreme Court.

Katyal, the former acting solicitor general in the Obama administration, asked the justices in Monday’s filing to hear Hidalgo’s case, and to strike down Arizona’s death penalty law.

The filing comes more than two years after Justice Stephen Breyer, joined by Justice Ruth Bader Ginsburg, called for a wholesale review of the constitutionality of the death penalty. Justice Sonia Sotomayor has also expressed great concerns about the courts’ handling of death penalty cases, as well as some states’ death penalty laws.

And Justice Anthony Kennedy has expressed concerns about the death penalty’s imposition, and has cast key votes excluding groups of people — like children and the intellectually disabled — from being eligible for the death penalty. He has not, however, given any specific indication that he is ready to join Breyer’s call to review the constitutionality of the death penalty overall — and has allowed several executions to proceed since Breyer's call.

Katyal, however, joined by other lawyers at his firm, Hogan Lovells, as well as by Susan Corey and others at the Office of the Legal Advocate in Arizona, and Arizona attorney Garrett Simpson, thinks the time is now — a move that could be tied to concerns by many liberal lawyers about whether and when Kennedy, at 81, might retire from the court.

“I have spent the last few years with my team looking for cases that highlight the gross problems with the death penalty in practice, and this case is a perfect example of them,” Katyal told BuzzFeed News on Monday evening. “We look forward to the Supreme Court's review of Mr. Hidalgo's petition.”

In 1972, the Supreme Court found the death penalty in America to be unconstitutional as then implemented. Four years later, in Gregg v. Georgia, the court brought it back — with new constraints — by approving several states’ new laws. In Monday’s filing, Katyal wrote of that case, “[T]he Court acknowledged that it might someday revisit the constitutionality of the death penalty in light of ‘more convincing evidence.’”

He continued: “The evidence is in. The long experiment launched by Gregg — in whether the death penalty can be administered within constitutional bounds — has failed. It has failed both in Arizona in particular and in the Nation more broadly.”

The brief points out that the court in Gregg found the new state death penalty laws to be constitutional because they required the finding of “aggravating” circumstances — a move that the court’s controlling opinion concluded would “direct and limit” who was eligible for execution “so as to minimize the risk of wholly arbitrary and capricious action.”

Forty years later, Arizona’s death penalty law is such that there are so many aggravating circumstances that “every first degree murder case filed in Maricopa County in 2010 and 2011 had at least one aggravating factor,” making the person eligible for the death penalty. Hidalgo pleaded guilty in 2015 to two January 2001 murders in a murder-for-hire scheme in Maricopa County. He was then sentenced to death by a jury.

“Arizona’s scheme utterly fails,” Katyal wrote, to “genuinely narrow the class of persons eligible for the death penalty” as the court has required over the time since Gregg.

For this reason alone, Hidalgo’s legal team argues, the court should take the case and strike down Arizona’s death penalty law.

But beyond that, the filing goes on, “A national consensus has emerged that the death penalty is an unacceptable punishment in any circumstance.” The brief argues that the court should take the case and rule that the death penalty, nationwide, is unconstitutional under the Eighth Amendment’s guarantee against cruel and unusual punishment.

This is so, the brief argues, because “the number of death sentences imposed and carried out has plummeted.”

The brief also points to three further key arguments in support of this larger aim: First, states can’t give guidance that ensures that only “the worst offenders” are sentenced to death. Second, states can’t enforce the death penalty without “ensnaring and putting to death the innocent.” And finally, “the present reality of capital punishment” — decades spent on death row with “the remote but very real possibility of execution” — is its own possible constitutional violation.

Hidalgo’s is not the first death penalty case Katyal’s team had considered taking to the Supreme Court. In the fall of 2015, just months after Breyer and Ginsburg’s statement about reviewing the death penalty, Hogan Lovells took on representation of Julius Murphy, who was on death row in Texas. The Texas courts, however, put that execution on hold indefinitely before the Hogan Lovells team had a reason to take the case to the US Supreme Court.