Igusa variety

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[1] and Igusa varieties were introduced by Harris and Taylor[2] for studying the bad reduction of some Shimura varieties: the ℓ-adic cohomology of Igusa varieties sheds some light on that of Shimura varieties.

References

  • Harris, Michael; Taylor, Richard (2001). The Geometry and Cohomology of Some Simple Shimura Varieties. Annals of Mathematics Studies. Vol. 151. Princeton University Press. ISBN 978-0-691-09090-0. MR 1876802.


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