mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, an Igusa curve is (roughly) a coarse

moduli space In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spac ...

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 and Igusa varieties were introduced by 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

* * Algebraic geometry Elliptic curves {{numtheory-stub