ExxonMobil's investor fraud trial is nearing a close, after two weeks of testimony from executives, investors and expert witnesses. The oil company stands accused of defrauding investors by misleading them about the risks the business faces from climate change, in civil charges brought by the office of New York Attorney General Letitia James.

With only days left before the two sides deliver their closing arguments, here's a look at what the attorney general needs to prove and how Exxon is fighting the claims.

What does the New York attorney general need to show in order to win?

The case was brought under New York's Martin Act, which gives the attorney general broad powers to investigate financial fraud. Lawyers for the state will have to convince Justice Barry Ostrager, who will decide the case, that Exxon made materially misleading statements—in other words, statements that an investor would likely have found important when deciding whether to buy or sell a stock, and that were false.

The attorney general is also asking the judge to award damages. To win such a ruling, the state will have to show that the statements affected Exxon's value.

Even if the attorney general can't establish this impact on the company's value, the judge could choose to issue an injunction, ordering Exxon to correct its disclosures, without awarding damages.

How has the AG's office tried to show that Exxon misled investors?

The state's lawyers have pointed to the company's public reports, disclosures and statements by its executives that said Exxon was accounting for the risks of climate change by applying a "proxy cost"—used to estimate the financial impact of future climate regulations—consistently across its business.

In fact, Exxon had a second set of lower estimates for these financial impacts that it used internally but did not disclose to investors, the attorney general alleges. (Applying a lower estimate for carbon costs had made high-emissions projects, like those in Canada's tar sands, where Exxon is a top producer, appear like more attractive investments.)

Exxon's disclosures made no mention of this second estimate—which it called a "greenhouse gas cost"—save for a report it issued in March 2014.

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The attorney general's lawyers have asked Exxon witnesses about a presentation that a senior manager gave to top executives in May 2014 that recommended the company align the lower greenhouse gas cost used internally with the higher proxy cost.

Notes from that presentation gave two reasons for making this change, both of which bolster the attorney general's case.

First, the notes said, the lower estimate did not provide a conservative assessment of regulatory costs in the future—such low-balling would make a new oil project appear more financially attractive. The notes also said that in recent reports Exxon issued to investors—including the March 2014 report with a one-sentence reference to greenhouse gas costs—the company implied that it was using the higher proxy cost in certain internal evaluations when it actually had used the lower greenhouse gas figure.

Several Exxon executives, including former chief executive Rex Tillerson, have testified that they don't recall any discussion that matches the notes from 2014. Some have testified that corporate managers decided to align the costs because of how they saw global climate policies shifting long-term.

How has Exxon tried to discredit the AG's claim?

Exxon's lawyers, and executives on the witness stand, have maintained that this system of using two different estimates was entirely legitimate and was, in fact, well thought out and robust.

The proxy cost was used to model global demand for oil and gas, and therefore future prices, they said. The lower greenhouse gas cost was meant to estimate the regulatory costs the company might face at specific projects—these were dependent on particular countries' carbon-cutting policies, or even those of particular state or local governments.

The attorney general's entire case, Exxon's lawyers have argued, is based on a misunderstanding of how the company runs its business.

Plus, executives have said on the stand, the company did disclose to investors that it used something it called a greenhouse gas cost, in one sentence in a report.

The paragraph mentioning a greenhouse gas (GHG) cost in the 2014 Exxon report “Energy and Carbon - Managing the Risks.”

Lawyers for the attorney general have countered that it's implausible to argue that this one sentence provided adequate disclosure. They have established that even some high-ranking Exxon managers did not understand the distinction in terminology between "greenhouse gas costs" and "proxy costs." Exxon's external auditor, Richard Auter at the firm PwC, admitted to having used the two terms interchangeably in a memo, even after meeting with Exxon's corporate greenhouse gas manager to discuss the topic.

How then, the attorney general's lawyers have asked, could investors with no knowledge of the company's internal practices be expected to parse the difference based on one sentence in one report?

Exxon's lawyers have also pointed to repeated instances in their disclosures where the company said that it does not reveal its proprietary business assumptions. In other words, they argued that investors were warned that the company wouldn't disclose all the estimates it used internally.

How has the attorney general tried to establish that any of this mattered to investors?

The attorney general's lawyers have pointed to testimony by an activist investor, a representative of New York City's pension funds and a market analyst who say they had concluded—wrongly, it now turns out—that Exxon was using its public proxy cost to assess the expenses it would face at specific projects, like a refinery.

Its lawyers have pointed to reports and memos by some investors—including Vanguard, Exxon's largest shareholder—that expressed concern about the risks posed by climate change, both to the energy industry in general and to Exxon specifically.

Finally, the attorney general hired two expert witnesses to establish a link between the disclosures the company made and financial markets. One witness, Peter Boukouzis, a former investment banker, ran a search through reports written by market analysts who track Exxon and found 99 reports that he said discussed climate change risks or proxy costs.

Boukouzis also did an analysis to argue that Exxon's alleged misdeeds cost investors between $476 million and $1.6 billion, numbers on which Exxon's lawyers cast doubt.

Exxon's legal team took apart much of Boukouzis's testimony. They questioned his assertion that market analysts were following Exxon's climate disclosures and pointed out holes in other work Boukouzis had performed for the attorney general—an analysis of Exxon's internal business models—that they said indicated he didn't fully understand the models he was analyzing.

Exxon's lawyers also presented a report from their own expert witness, Marc Zenner, who ran a similar search of market analyst reports and found only two to have specifically discussed proxy costs. In both cases, Exxon pointed out, the analyst continued to rate the company's stock favorably.

More generally, Exxon has been making the case that there was no impact to its finances no matter whether it applied a higher or lower estimate for the future cost of carbon emissions.

Its lawyers have argued that the attorney general's office has failed to identify a specific oil or gas project investment decision that would have been swayed by applying the higher cost, or any other way the difference would have affected corporate earnings. In other words, its lawyers are saying, whether or not the company misled investors, the practice had no impact on its value, or on how investors assessed the company.

What might a verdict mean?

Exxon faces potential damages that could reach into the hundreds of millions or even billions of dollars (for perspective, its earnings last year were $20.8 billion). It could also be ordered to correct its disclosures to investors, which would be a win for the growing movement to improve financial disclosures around climate change.

John Coffee, a professor and director of the Center on Corporate Governance at Columbia Law School, said that a ruling against Exxon would put other companies on notice about what they must disclose to investors, too.

"Because this is a case involving standards that really have never been tried before," he said, "a decision favoring the attorney general is going to cause a lot of concern to other companies."

If Exxon prevails, that could discourage other efforts to try to go after companies for their climate disclosures, said Michael Gerrard, who runs the Sabin Center for Climate Change Law at Columbia University. The oil giant already faces a second fraud lawsuit filed last month by the Massachusetts attorney general.

"Because so much information about Exxon has come out," he said, "if the (New York) attorney general can't ultimately lay a claim, that would be a bad sign for such future litigation."