Abstract
To thememory of Robert Coleman *Correspondence: deshalit@math.huji.ac.il 1Hebrew University, Jerusalem, Israel Full list of author information is available at the end of the article
Highlights
1.1 The unitary group and its symmetric spaceLet K be an imaginary quadratic field, contained in C
When we introduce the Shimura variety later on, we shall relax this last assumption, but the resulting scheme will be disconnected
Γ : VR → VR intertwines the complex structures xg and xγ g, and carries Lg to Lγ g, so induces an isomorphism of the abelian varieties, which clearly commutes with the PEL structures
Summary
Let K be an imaginary quadratic field, contained in C. We denote by Σ : K → C the inclusion and by Σ : K → C its complex conjugate. √ dK—the square-free integer such that K = Q( dK). ΔK = DK—the square root with positive imaginary part, a generator of the different of K, somet√imes denoted δ. We fix an integer N ≥ 3 (the “tame level”) and let R0 = OK[1/(2dKN )]. M(Σ )) is the part of M on which OK acts via Σ The same notation will be used for sheaves of modules on R-schemes, endowed with an OK action.
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