Mathematics – Algebraic Geometry
Scientific paper
2009-02-19
Mathematics
Algebraic Geometry
v2: Important references added. New example by David Harbater: the group scheme structure on the additive group does not lift
Scientific paper
In topology, the notions of the fundamental group and the universal cover are closely intertwined. By importing usual notions from topology into the algebraic and arithmetic setting, we construct a fundamental group family from a universal cover, both of which are schemes. A geometric fiber of the fundamental group family (as a topological group) is canonically the 'etale fundamental group. The constructions apply to all connected quasicompact quasiseparated schemes. With different methods and hypotheses, this fundamental group family was already constructed by Deligne.
Vakil Ravi
Wickelgren Kirsten
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