A federal judge ruled Tuesday against the U.S. government's proposal that Google should sell its Chrome web browser to restore competition in online search.

The highly watched decision came after a three-week hearing that concluded in May, in which lawyers for the U.S. government and Google argued over how to fix the tech giant's search monopoly.

The shares of Google's parent company, Alphabet, surged in after-hours trading following the announcement.

Last year, it was ruled that Google illegally maintained a monopoly in online search, pointing to exclusive agreements the company struck with Apple, Samsung, AT&T and others to be the default search engine on web browsers and mobile devices. Google, based in Mountain View, Calif., disagreed with the ruling.

The Department of Justice and several states proposed several ways to fix Google's monopoly, including forcing the company to sell Chrome, a web browser the agency described as the "gateway to the internet."

Google said the government's proposal went too far and would harm consumers and America's technological leadership. Instead, the company suggested more narrow solutions that would make its contracts with wireless carriers and mobile device makers less restrictive.

The antitrust case stems from a lawsuit the DOJ and multiple states filed against Google in 2020, under the Trump administration, alleging it illegally operated as a monopoly.

Since then, online search has evolved, with more people turning to short videos and AI chatbots like ChatGPT to find information or summarize search results.

Google has been trying to race ahead as OpenAI, Meta and others compete to dominate AI. Google shows AI-generated summaries of search results, released an "AI mode" in search and has a virtual assistant called Gemini.

AI companies, including OpenAI in San Francisco, had expressed interest in buying Google Chrome ahead of the judge's decision. In August, AI startup Perplexity made a bold bid to purchase Google Chrome for $34.5 billion. (The Los Angeles Times partners with Perplexity to generate summaries of ideas expressed in opinion pieces.)

Alphabet, the parent company of Google, has continued to see its stock price rise this year despite uncertainty over Chrome's future. In the second quarter, Google's revenue reached $96.43 billion per year, up roughly 14% compared to the same period last year. The company's net income jumped 19% to $28.19 billion.

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