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Grenoble, France (CNN)-- Dozens of fans gathered Friday outside the French hospital treating former racing driver Michael Schumacher, keen to show their support as he lies in a coma on his 45th birthday.

Schumacher suffered severe head trauma in a skiing accident in the French Alps on Sunday.

Since then, he has undergone two operations and is said to be in stable but critical condition at the hospital in Grenoble city.

Scuderia Ferrari, the racing team division of the Italian carmaker, urged fans to join the vigil outside his hospital via its Facebook page.

People should dress in red, and it will be "a silent and respectful event," the page said.

Pauline Degot, 19, from France, told CNN, "It's important to show support to Schumacher on his birthday and especially when he needs us most."

Seventeen-year-old Italian Ferrari fan Marco Raccanello, using the driver's nickname, said, "I've watched Schumi since I was a little boy and it means a lot to be here today."

Some supporters joined together to display a huge Ferrari flag, while others carried banners with messages of encouragement for Schumacher. "Schumi, all our thoughts for you and your family," read one.

The driver's family and Ferrari praised his fighting spirit as he battles to overcome his injures.

"We would like to thank the people from all around the world who have expressed their sympathy and sent their best wishes for his recovery. They are giving us great support," his family posted on his official website.

"We all know he is a fighter and will not give up."

Ferrari, for whom Schumacher -- the most successful driver in Formula 1 history -- won 72 Grand Prix races between 1996 and 2006, also posted a birthday message on its website.

"This is a special day for Ferrari and all its fans, as it is Michael Schumacher's birthday," it said.

"At the moment, he is tackling the most important fight of his life and therefore we want to send him very special wishes."

Schumacher's manager, Sabine Kehm, said Wednesday that the driver was in a stable condition, but it's too early to speculate on his prospects for recovery.

He was catapulted headfirst onto a rock while skiing with family and friends in the resort of Meribel, she said.

On Monday night, doctors carried out a surgical intervention that relieved some pressure on his brain. They reported a slight improvement in his condition Tuesday, but he remained critically ill.

The University Hospital Center of Grenoble said doctors would not give an update Friday on Schumacher's condition unless it changed.

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