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 (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.

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
• Igusa, Jun-ichi (1968), "On the algebraic theory of elliptic modular functions", Journal of the Mathematical Society of Japan, 20: 96–106, doi:10.2969/jmsj/02010096, ISSN 0025-5645, MR 0240103