Introduction to Shimura Varieties

By J. S. Milne. 2004

251 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/96ed1227a8404308ffedd2672befd7e0308e1ca2

Citations in the corpus

• Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type (2013, unknown): “We will ûrst follow [13] to introduce Shimura varieties, and then follow [7] to introduce integral canonical models.”
• Period Mappings and Period Domains (2017, unknown): “This approach can be found in Milnor and Stasheff (1974). This leads, for instance, naturally to the interpretation of the Euler number as the highest Chern class of the tangent bundle, as mentioned above. Then we have Grothendieck’s approach, which works well in algebraic geometry. We treat this ap”
• Applications of the hyperbolic Ax–Schanuel conjecture (2017, unknown): “1) is defined over E(GL2, H±) = Q, it suffices to bound the size of π0(ShK(GL2, H)), which, by [25], Theorem 5.”
• Galois orbits and equidistribution of special subvarieties: towards the André-Oort conjecture (2012, unknown): “3(a) of [13], E(H,XH) is contained in any splitting field of H.”
• CM points and quaternion algebras (2005, unknown): “We now want to describe the reciprocity laws for CM points and connected components, following [14] instead of [4] (see the remark at the end of [14, §12]).”
• Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication (2007, unknown): “Since the center of GSp(V,Q)R is given by Gm,R (see [40], page 66), the kernel of the adjoint representation on Lie(GSp(V,Q)R) of any h(S) in the conjugacy class is given by Gm,R.”
• The André-Oort conjecture (2012, unknown): “For details on this definition, sketches of proofs of the existence and uniqueness and all the relevant references we refer the reader to Chapters 12-14 of [21].”
• Local models of Shimura varieties, I. Geometry and combinatorics (2010, unknown): “, Shimura varieties of “abelian type” [71, 70] produce pairs that support such symplectic representations.”
• Ax-Schanuel for Shimura varieties (2017, unknown): “We refer to [8, 9] or [23] for a detailed introduction to Shimura varieties.”
• Shimura Varieties and Moduli (2011, unknown): “See [40], §5, for proofs of the statements in this subsection.”