Universal covering spaces and fundamental groups in algebraic geometry as schemes
نویسنده
چکیده
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 étale fundamental group. The constructions apply to all connected quasicompact schemes; we needn’t work over a field. Noetherian hypotheses don’t need to be removed after the fact; they are not there from the start. CONTENTS
منابع مشابه
Universal Covering Spaces and Fundamental Groups in Algebraic Geometry as Schemes
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 étale fundamental group. The ...
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تاریخ انتشار 2009