In mathematics, an Igusa curve is (roughly) a coarse moduli space of elliptic curves in characteristic p with a level p Igusa structure, where an Igusa structure on an elliptic curve E is roughly a point of order p of E(p) generating the kernel of V : E(p) → E. An Igusa variety is a higher-dimensional analogue of an Igusa curve. Igusa curves were studied by Igusa and Igusa varieties were introduced by Harris and Taylor for studying the bad reduction of some Shimura varieties: the -adic cohomology of Igusa varieties sheds some light on that of Shimura varieties.
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