SAN FRANCISCO >> Yahoo began closing ranks behind its abruptly reshuffled leadership team Monday, but the company stayed mum on how it would proceed after firing its second CEO in the past eight months.

The Sunnyvale, Calif., Internet giant, which fired CEO Scott Thompson on Sunday after he was revealed to have falsely claimed he earned a computer science degree, filed formal notice of the separation agreement Monday with the Securities and Exchange Commission.

The filing revealed that Thompson, who was earning an annual salary of $1 million, will not receive severance pay for his five months at the helm of the 12,000-person company. But he will receive cash and stock given him to compensate for money he gave up this year when he left eBay, where he was in charge of the PayPal division.

Those awards are worth about $6.5 million, according to the Wall Street Journal, which also reported that Thompson was recently diagnosed with thyroid cancer.

The SEC filing also includes an agreement that Yahoo and Thompson will not disparage each other publicly. The company, which has hired a crisis communications firm to manage inquiries, declined to comment on issues surrounding the CEO transition.

The spotlight now turns to Ross Levinsohn, formerly Yahoo’s executive vice president of the Americas, who took over as CEO on an interim basis but is said to be auditioning for the top job. He will be charged with reversing declines in Yahoo’s core advertising business amid tough competition from Google and Facebook and an exodus of talent that accelerated this spring with the layoffs of 2,000 people.

Levinsohn was hired by Thompson’s predecessor, Carol Bartz, who was fired in September amid concerns that her turnaround plan was not producing results quickly enough. Levinsohn previously was president of News Corp.’s digital division, Fox Interactive Media, where he oversaw the acquisition of MySpace and IGN, among other large Web properties.

Before joining Fox, Levinsohn served in senior management at online search company AltaVista and also worked at CBS Sportsline and HBO Inc. He holds a bachelor’s degree in communications from American University.

In a memo to employees Sunday, Levinsohn assured them that Yahoo is “heading in the right direction,” and urged employees to “focus on the momentum” the company has gained in recent months.

But Yahoo’s future will not rest entirely in Levinsohn’s hands. The interim CEO also faces a radically remade board that includes three new faces — people who pointedly disagreed with Yahoo’s direction under Thompson.

The new board members are activist shareholder Daniel Loeb and two people he asked to join him, Harry Wilson and Michael Wolf. Loeb, founder of hedge fund Third Point LLC, triggered Thompson’s departure by publicizing the error in his biography to the SEC and the media.

Loeb issued a statement Sunday saying “we are committed to working with new leadership to unlock Yahoo’s significant potential and value,” likely a reference to a sale of some of the company’s assets. Most of Yahoo’s market value derives from its large stakes in successful Asian Internet businesses, and some investors have been clamoring for Yahoo to sell them off.

Third Point, which agreed to abandon a planned proxy fight against Yahoo in exchange for getting the three board seats, declined to comment on board members’ plans for the company. They also shut down a website they set up to criticize Thompson and former board members, valueyahoo.com.

Given the uncertainty around the CEO position at Yahoo, the board is expected to play an especially strong role in setting a course for the company.