Could a desert form at 45°n latitude

Yes

Explanation:

Some deserts are formed due to the movement of hot air masses and the lack of moisture from the tropics, influenced by the Earth's rotation. These masses, after cooling in the atmosphere and curving north and south, begin to lose latitude up to approximately 30 °, however, they gain heat from the descent by increasing their ability to retain and "absorb" the available water in the soil. These deserts are between 30 ° to 50 ° (north / south). Examples are the Sahara Desert in Africa and Soonora in North America.

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