David Perdue finding a niche as the anti-democracy candidate in Georgia.

Former Senator David Perdue of Georgia, a Republican who is running for governor with the backing of former President Donald J. Trump, filed a lawsuit on Friday seeking the inspection of absentee ballots in the 2020 election, reviving long-debunked claims in the latest sign that Mr. Trump’s election grievances will be central to his candidacy.

The lawsuit draws on Mr. Trump’s false claims of election fraud in Georgia and across the country, which culminated in the Capitol riot on Jan. 6. In the months since, many Republican elected officials have pivoted from rebuking election conspiracy theories to embracing them vocally in an effort to win the affections of Mr. Trump and his supporters.