Generalizing both algebraic varieties and arithmetic objects, schemes play a central role in the unification of ideas from Algebraic Geometry and Number Theory. Goal of this study group is to work with schemes for the first time, try to get a grasp of what they can and cannot do, and begin to study their properties (development of study material is open-ended). If we are thorough, we might at the end be able to keep up a conversation with an algebraic geometer by doing more than just nodding and smiling.

For the main source we would use Ravi Vakils "The Rising Sea: Foundations of Algebraic Geometry" (hence the title), using Eisenbud's "Geometry of Schemes" as supplement ans also maybe Hartshorne because it is such a classic.