Q. Shimura varieties are not algebraic varieties but are families of algebraic varieties. Shimura curves are the one-dimensional Shimura varieties. Hilbert...

theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the Taniyama–Shimura conjecture which ultimately led to the...

mathematician Shimura correspondence Eichler–Shimura congruence relation Shimura variety Hitomi Shimura (紫村 仁美, born 1990), Japanese hurdler Ken Shimura (志村 けん...

over the finite field Fp. The Eichler–Shimura congruence relation and its generalizations to Shimura varieties play a pivotal role in the Langlands program...

The modularity theorem (formerly called the Taniyama–Shimura conjecture, Taniyama–Shimura–Weil conjecture or modularity conjecture for elliptic curves)...

more general statement (albeit with a restriction on the type of the Shimura variety) was conjectured by Frans Oort in 1995. The modern version is a natural...

Compactifications and cohomology of modular varieties. In Harmonic analysis, the trace formula, and Shimura varieties, volume 4 of Clay Math. Proc., pages 551–582...

Pink proposed (again independently) a more general conjecture for Shimura varieties which also implies the André–Oort conjecture. In the case of algebraic...

introduced the varieties in 1943. Siegel modular varieties are the most basic examples of Shimura varieties. Siegel modular varieties generalize moduli...

and the l-adic Galois representations. The Shimura variety theory is related, by the idea that such varieties should parametrize not just good (arithmetically...