Larry Page era's first exit: Product Chief Jonathan Rosenberg

One day into Page-run Google, there is already a high-profile departure.

The San Jose Mercury News today reports that Senior VP of Product Management Jonathan Rosenberg just resigned from Google(GOOG).  Earlier today, SAI ranked him the 4th most powerful exec under the new regime of Larry Page though he ranks about ninth on the current official list.

The soft angle is that, "Rosenberg wanted to work at Google until his high school-aged daughter left for college, but that new Google CEO Larry Page wanted longer term commitments from his senior executives."

"We tried to hire Jonathan multiple times because he was the only person we could imagine doing the job. It's lucky we were so persistent because he's built an amazing team—hiring great people, who've created amazing products that have benefited over a billion users around the world," new CEO Larry Page said in a prepared statement.

But we're all adults here.  You don't depart on the day of a CEO switchover unless there are some disagreements at the top.

Rosenberg was an early manager brought in under Eric Schmidt, but he's probably most famous in and around Google for penning Google's"Meaning of  Open" in 2009.

Today, he told the Mercury news:

"I think I've done the things that I set out to do. My focus has been on building a great team, and hiring the best people in the world. I think I've also been very focused in studying the manner in which we manage at Google, and working very hard on developing the next set of Google management talent," Rosenberg said. "We're obviously going through a transition here; Larry is stepping into the role of CEO. And I think it was important to him that he establish and build around an executive team that intended to be here for many, many years."

He will stay with Google throughout the summer and continue to do consulting for Google after that.  According to the Mercury News he's also going to help his old boss Eric Schmidt with his book on the Google management style.

Rosenberg was a veteran of Excite @home and Apple's (AAPL) eWorld before he joined Google almost a decade ago.