An F.B.I. search warrant affidavit unsealed on Tuesday shows that a criminal investigation into 2020 election results in Fulton County, Ga., was set off by a leading election denier in the Trump administration and relied heavily on claims about ballots that have been widely debunked.

The unsealing of the affidavit in Fulton County is likely to raise more questions about the Trump administration’s use of the F.B.I. and Justice Department to revive old, largely disproved claims about the 2020 election in the state, which President Trump narrowly lost.

“The FBI criminal investigation originated from a referral sent by Kurt Olsen, Presidentially appointed Director of Election Security and Integrity,” the affidavit said. Mr. Olsen played a central role in Mr. Trump’s attempt to overturn the 2020 election, including speaking to the president multiple times on Jan. 6, 2021. He has continued to push false claims about elections, and was recently appointed to a key role in the Trump administration.

Many of the claims in the affidavit refer to long-held — and consistently debunked — conspiracy theories about elections in Georgia, including arguments about fraudulent and duplicate absent ballots, election machine tabulator tapes and missing ballot images. ....

In a court filing last week, Fulton County pointed to the many debunked conspiracy theories and previous investigations as a reason that the affidavit should be unsealed.

“The continued perpetuation of these unfounded allegations sows distrust around both judicial and electoral processes in Fulton County and the state of Georgia,” the county wrote. “Transparency is necessary to ensure public knowledge and confidence. At a minimum, the public has a right to know what its government is doing.”