The lawsuit said that “this fraud reached the highest levels of the company,” including former Exxon chief executive and former secretary of state Rex Tillerson, who the lawsuit said knew for years that the company “was deviating” from public statements and was using two sets of calculations about future regulation of greenhouse gas emissions.

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“The attorney general is effectively charging them with keeping two sets of books — one for internal purposes, one for external,” said Tom Sanzillo, director of finance at the Institute for Energy Economics & Financial Analysis, which conducts research on energy and the environment. “The result is a distortion of the value of the company.”

ExxonMobil spokesman Scott J. Silvestri called the lawsuit meritless. “These baseless allegations are a product of closed-door lobbying by special interests, political opportunism and the attorney general’s inability to admit that a three-year investigation has uncovered no wrongdoing.”

The lawsuit says that ExxonMobil’s dual accounting calculations had a huge impact on the purported value of the company. It says that the company’s failure to apply an internal price on carbon at 14 of its oil sands projects in Alberta, Canada resulted in undercounting future greenhouse gas expenses by more than $25 billion over the lifetime of the project. It also said that the oil giant did not apply any such proxy costs to the company’s reserves at Cold Lake, a major oil sands asset in Alberta, “resulting in an overestimation of its projected economic life by 28 years.”

Earlier lawsuits against big oil companies alleged that they had concealed internal and private studies confirming climate change and human contributions to it, but lawsuits seeking damages have been thrown out of court.

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ExxonMobil has also taken small steps to polish its image on climate change. It recently contributed $100 million to a fund that provides money to new technologies that would slash greenhouse gases. And it gave $1 million to a prestigious group of economists and former public officials that backs a carbon tax starting at $40 a ton.

The New York attorney general’s suit zeros in on the company’s financial reporting.

“Exxon told investors that it accounted for the risk of governmental regulation of climate change by applying a ‘proxy cost’ of carbon,” the attorney general’s office said in a statement. “Exxon told its investors that it used that proxy cost in its investment decisions, corporate planning, estimations of company oil and gas reserves, evaluations of whether its long-term assets remain viable, and estimations of future demand for oil and gas.”

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Yet, the complaint alleges, “Exxon frequently did not apply the proxy costs as represented in its business activities. Instead, in many cases Exxon applied much lower proxy costs or no proxy cost at all.”

The lawsuit seeks an order prohibiting Exxon from misrepresenting its climate calculations and requiring it to correct its misrepresentations — “in other words, to tell investors the truth.”

The suit also asks the court to award damages and restitution associated with the alleged fraud.

“Estimating climate-related liabilities is ‘more art than science’ because of how long-term and uncertain the calculations are,” Pavel Molchanov, a securities analyst at Raymond James, said in an email. “Unless the New York AG has textual, documentary evidence of deliberate deceit on the part of management, it will be difficult to prove the case.”

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Molchanov said that “the vast majority of retail investors have no awareness of this issue, because it is so technical.” He added that among “institutional investors, there is greater awareness, though I doubt this issue would be decisive either way.”