Supreme Court takes the bench with ghost guns, a capital case and transgender rights on the docket

He then gaveled in the start of the court's new term. The docket isn't as packed, but the conservative-majority court could yet be asked to intervene in election disputes after the ballots are cast in November.

The justices then heard their first case dealing with pandemic-era unemployment claims filed in Alabama.

The term's beginning comes after a relatively busy summer hiatus for the court. The orders they issued on emergency appeals included a refusal to restore President Joe Biden's student loan plan and a partial approval of an Arizona law requiring proof of citizenship to vote.

The new term opens against the backdrop of low public trust in the Supreme Court, and continued debate about whether its newly adopted code of ethics should have an enforcement mechanism.

Here's a look at some of the cases coming up:

Ghost gun regulations

The justices will hear a case Tuesday on regulations for ghost guns, privately made weapons that are hard for police to track because they don't have serial numbers.

The number of the firearms found at crime scenes has soared in recent years, from fewer than 4,000 in 2018 to nearly 20,000 recovered by law enforcement in 2021, according to Justice Department data.

The numbers have been declining in multiple cities since the Biden administration began requiring background checks and age verification for ghost gun kits that can be bought online.

But manufacturers and gun rights groups argue that the administration overstepped and the rule should be overturned.

Doubts about a death sentence

In the decades since Richard Glossip was sentenced to die over a 1997 murder-for-hire scheme, the case has become a rare one where prosecutors are conceding mistakes.

Oklahoma's Republican attorney general has joined with Glossip in seeking to overturn his murder conviction and death sentence.

Despite those doubts, an Oklahoma appeals court has upheld Glossip's conviction, and the state's pardon and parole board deadlocked in a vote to grant him clemency.

The court will hear arguments in his case on Wednesday.

Transgender rights

Perhaps the court's most closely watched case so far this year is a fight over transgender rights.

The case over state bans on gender-affirming care comes as Republican-led states enact a variety of restrictions, including school sports participation, bathroom usage and drag shows.

The administration and Democratic-led states have extended protections for transgender people, though the Supreme Court has separately prohibited the administration from enforcing a new federal regulation that seeks to protect transgender students.

The justices will weigh a Tennessee law that restricts puberty blockers and hormone therapy for transgender minors. The case does not yet have a hearing date but will likely be argued in December.