While the White House and Congress are embroiled in questions of possible presidential abuse of power and the start of an official impeachment inquiry, the Supreme Court’s new term will open with weighty issues involving gun restrictions, LGBTQ workplace rights, religious school funding and the fate of so-called Dreamers.

The nature of the issues and the possibility of a number of decisions resulting in ideological 5-4 splits may thrust the high court repeatedly into the public eye during the 2020 election season and offer fodder to presidential candidates, some of whom already have been talking about “reforming” the Supreme Court.

Whether intentionally or not, the justices largely succeeded last term in keeping a relatively low profile following the bitter confirmation battle over the nomination of Justice Brett Kavanaugh. They decided few blockbuster cases and the term was notable for the number of unusual voting crossovers by justices on the left moving right and vice versa.

The nature of the issues and the possibility of a number of 5-4 decisions may thrust the high court repeatedly into the public eye.

That feat will be difficult to match during the term beginning Oct. 7. The cases already slotted for decision could reveal the justices’ deepest disagreements.

The justices continue to add cases to the term’s decision docket until about mid-January. Waiting in the wings are multiple petitions related to issues on guns and abortion. And moving through the lower court pipeline are cases involving border wall funding, new asylum restrictions, emolument clause cases against President Donald Trump, and the president’s challenges to congressional subpoenas for his financial records.

Although John Roberts Jr. has been chief justice since 2005, the Roberts Court is very much a work in progress. The retirement of Justice Anthony Kennedy, a crucial and often decisive vote in the closest cases, has shifted the court’s center to Roberts, a more conservative justice. And the recent additions of Justices Neil Gorsuch and Brett Kavanaugh create uncertainty about where their jurisprudence will take them.

Here are the cases being most closely watched as the term unfolds:

Insanity and unanimity

Two separate criminal cases raise questions that many of us might have thought were settled long ago. In Kahler v. Kansas, the justices will hear arguments Oct. 7 on whether the Eighth and 14th Amendments allow a state to abolish the insanity defense. The Trump administration, in an amicus brief, supports Kansas, which argues that the Constitution allows states to decide how mental states should be considered in criminal law. And on the same day, in Ramos v. Louisiana, the high court will hear arguments on whether the Sixth-Amendment guarantee of a unanimous jury verdict to convict someone applies to the states. Only Louisiana and Oregon permit non-unanimous juries.

LGBTQ rights

The justices will hear three workplace discrimination cases involving the federal law prohibiting employers from discriminating because of sex. Two of the three cases ask whether “because of sex” includes discrimination because of sexual orientation, and the third case questions whether that same language bars discrimination because of transgender status or sex stereotyping. These cases will be argued Oct. 8

READ MORE: Does this anti-discrimination law protect LGBTQ workers? 3 cases ask Supreme Court to decide

Puerto Rico debt

The justices have five cases, joined for oral arguments, involving the appointment of members of the Puerto Rico Financial Oversight and Management Board, which is responsible for restructuring Puerto Rico’s massive debt. A federal appellate court ruled that the appointments violated the Constitution’s appointments clause. The financial stakes of the outcome are enormous. Arguments are on Oct. 15.

Dreamers

The Trump administration wants to end the Deferred Action for Childhood Arrivals program, or DACA, created by the Obama administration as a temporary deferral of deportation of certain young people brought to this country by their undocumented parents. In Department of Homeland Security v. Regents, University of California, the justices will hear three cases consolidated for argument in which lower courts decided that the Trump action violated the federal Administrative Procedures Act. Arguments are on Nov. 12.

Cross-border shooting

Mexican teenager Jesus Hernandez was unarmed and hiding behind a pillar in the culvert between the United States and Mexico when he was shot and killed by a U.S. border patrol officer. His family is asking the high court if federal courts can recognize a damages claim for the agent’s actions. Arguments are also scheduled for Nov. 12.

Religious funding

In Espinoza v. Montana Dept. of Revenue, the high court will decide whether a Montana scholarship program that bars the use of its funds at religious schools, consistent with a prohibition in its state constitution, violates the U.S. Constitution’s religion clauses or equal protection clause. No argument date has been set yet.

Guns

The justices have been extremely reluctant to wade back into the Second Amendment since their landmark 2008 decision in District of Columbia v. Heller, establishing an individual right to possess a firearm in the home for self-defense. Justice Clarence Thomas has strongly criticized his colleagues for that reluctance and has called the Second Amendment a “constitutional orphan.”

READ MORE: The Supreme Court could take on these 2 major gun lawsuits. Here’s what to watch

But at least four justices were willing to vote to grant review to N.Y. State Rifle and Pistol Assn. v. City of New York, to be argued Dec. 2. The challenge is to the city’s ban on the transport of licensed and unloaded guns outside the city limits. But there is a big wrinkle in the case. The city changed its rules over the summer and argues the case is now moot because it has given the challengers all that they sought. Stay tuned on this one.