European markets head into Tuesday after a strong start to the week, with investors waiting for US inflation data that could decide whether the recent rally in shares has further to run.

On Monday, the pan-European Stoxx 600 rose 1.3%, while London's FTSE 100 added 1% to close at 10,782.87. In Europe, the CAC 40 in Paris rose 1.2% and the DAX 40 in Frankfurt climbed 1.7%. The gains came as a sharp fall in oil prices eased inflation worries and as hopes of a diplomatic breakthrough in the US-Iran conflict lifted sentiment.

The mood is cautious rather than euphoric, however. The next big test arrives on Tuesday, when the United States publishes its October consumer price index (CPI), the last inflation reading before the Federal Reserve's December meeting.

Why the CPI print matters

Economists expect a 0.3% monthly rise in consumer prices, with core CPI, which strips out food and energy, forecast to rise 0.2%. The Bureau of Labor Statistics will not publish annual CPI figures for October, which makes the monthly numbers the main focus for traders.

The reading matters because it feeds directly into the debate over the Fed's next move. Commonwealth Bank economists have warned that a hot CPI reading could lift the odds of a December rate rise by the Fed, which would put pressure on shares and on currencies such as the Australian dollar. A cooler reading, by contrast, would support the rally that has carried markets higher this week.

September's figures ran hot on core inflation, rising 0.3% on the month for a second month in a row, while headline CPI rose 0.6% in the month, with energy accounting for more than half of the increase. That backdrop is why Tuesday's print is being treated as the week's defining event.

Wall Street's strong night

Wall Street posted its best session since April on Monday, as buyers returned to technology stocks and the drop in oil prices eased inflation concerns ahead of the CPI report. The S&P 500 rose 2.35%, the Nasdaq 100 added 3.4% and the Dow Jones gained 2.2%, while a gauge of chipmakers climbed almost 7%.

The gains came despite a sharp fall for chip maker Nvidia, as investors weighed an investigation into chief executive Jensen Huang's relationship with a woman suspected by US intelligence officials of spying for China. The episode was a reminder that company-specific risks can still unsettle even a strongly rising market.

In London, the pound was quoted at $1.3415 late on Monday afternoon, up from $1.3362 at the same time on Friday, as the dollar softened on falling energy prices and improving appetite for risk.

What else is on the calendar

Alongside the CPI release, due at 08:30 in New York, or 13:30 in London, Federal Reserve Governor Christopher Waller is due to speak later on Tuesday, offering the first market-moving comments from a Fed official after the data.

September's job openings figures are also due, and Germany's ZEW survey of economic sentiment will give an early read on confidence in Europe's largest economy. On the corporate front, Vodafone reports half-year results in London, a day after the telecoms group was already in focus ahead of its update.

For European investors, the calculation is straightforward: Monday's rally was built on cheaper oil and hopes of de-escalation. Whether it holds will depend on what Tuesday's inflation numbers say about the cost of living, and about how much room the Fed has to move next month.