President Donald Trump steps off his plane as he arrives at Paya Lebar Air Base in Singapore, ahead of a summit with North Korean leader Kim Jong Un, June 10, 2018.

There are also important U.S. data, including the consumer price index, which comes as the Fed begins its two-day meeting Tuesday, and retail sales on Thursday.

Both the Federal Reserve and European Central Bank meet in the week ahead, with the Fed's two-day meeting ending Wednesday and the ECB rate meeting Thursday. The Fed is expected to raise interest rates a quarter point, but the one to watch is the ECB, since it could signal an end to its quantitative easing, or asset purchases. That could have a wide-ranging impact on global interest rates, as European rates should begin to move higher.

But expectations are low for a detailed plan, laying out denuclearization on North Korea's part. Strategists mostly expect a positive spin and a prelude to future discussions and maybe even a promise to visit each other's capitals. Negative for markets would be if, for some reason, talks break down.

Markets are counting on a successful summit between President Donald Trump and North Korean leader Kim Jong Un when the two hold a historic meeting in Singapore on Tuesday.

Trade headlines could continue to dominate as the U.S. is talking trade with China but also was to have laid out a list of goods that will be tariffed by Friday. The G-7 leaders meeting was to have wrapped up over the weekend, and leaders were at odds with Trump over trade heading into that meeting.

Robert Sinche, chief global strategist at Amherst Pierpont, said the CPI could be a big market mover in the coming week, since his firm is expecting headline consumer inflation to rise to 2.9 percent year over year and core to reach 2.3 percent. "That [core] would match the highest since 2008," he said. "I think the combination of the ECB on Thursday, coming after the CPI number on Tuesday — and I think the CPI number could be the most important of all — it could be an interesting week not because of G-7 or North Korea."

The inflation number could, in fact, help swing a debate that many market pros are hoping will be resolved by the Fed on Wednesday, and that is whether it raises rates one or two more times this year, after the June hike.

The Fed forecast a total of three hikes this year, but many in the markets are betting on four. Last Friday's strong jobs report, with higher wage growth, added fuel to the latter view, and hotter inflation could be further confirmation.

Fed Chair Jerome Powell also briefs the media after the meeting, and there are some expectations he could give more clues about the path of rates this year.

"After the last meeting, where they sounded a little more dovish, I think it might be deemed to be hawkish, frankly," said Leo Grohowski, CIO of BNY Mellon Wealth Management.

Stocks finished the past week higher, with the S&P 500 up 1.6 percent at 2,779.

"'I think one of the reasons the market behaved this week is you're still basking in the glow of the good jobs numbers from last Friday. That said, I think I'm going to be more interested in the ECB," said Grohowski.

As for North Korea, the summit could be little more than a positive backdrop for markets that are focused on central bank actions and trade.

"I don't think it will be much in a market-moving sense, unless there's something on the fringes that's remarkably positive or remarkably negative," said Grohowski.