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 (1968) and Igusa varieties were introduced by Harris & Taylor (2001) with the motivation that they have application to studying the bad reduction of some PEL Shimura varieties, the ℓ-adic cohomology of Igusa varieties sheds some light on that of Shimura varieties.
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