A survey of Galois theory of curves in characteristic p

Details A survey of Galois theory of curves in characteristic p A survey of Galois theory of curves in characteristic p

2010-04-13

arxiv.org/abs/1004.2267v1

Mathematics

Algebraic Geometry

17 pages. Submitted to Fields Communication Volume WIN: Women in Numbers.

Scientific paper

This survey is about Galois theory of curves in characteristic p, a topic which has inspired major research in algebraic geometry and number theory and which contains many open questions. We illustrate important phenomena which occur for covers of curves in characteristic p. We explain key results on the structure of fundamental groups. We end by describing areas of active research and giving two new results about the genus and p-rank of certain covers of the affine line.

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