Which of the following styles was created by nineteenth-century west coast brewers using warm fermentation with lager yeast?

The style that was created by nineteenth-century west coast brewers using warm fermentation with lager yeast is California Common. This distinctive beer style emerged primarily in California during the Gold Rush era when brewers began to utilize lager yeast, which typically ferments at cooler temperatures, in warmer fermentation conditions to suit the local climate.

California Common is characterized by its use of a specific strain of lager yeast that can thrive at higher temperatures, producing a beer that is both crisp and refreshing, yet with more fruity and complex flavors than traditional lagers due to the warmer fermentation method. This innovation allowed brewers to create a beer that was well-suited to the environmental conditions of the West Coast while maintaining the lager style's refreshing qualities.

In contrast, American Lager and Pilsner both have different historical and geographical contexts, with American Lager typically being produced using cooler fermentation temperatures and techniques brought over from European brewing traditions. Amber Ale, on the other hand, is an entirely different style that is more aligned with ales and not related to the foundational characteristics that define California Common. This context illustrates the unique nature of California Common and how it fits into the development of American brewing culture.