Introduction | p. 1 |
Mumford-Tate Groups | p. 28 |
Hodge structures | p. 28 |
Mumford-Tate groups | p. 32 |
Mixed Hodge structures and their Mumford-Tate groups | p. 38 |
Period Domains and Mumford-Tate Domains | p. 45 |
Period domains and their compact duals | p. 45 |
Mumford-Tate domains and their compact duals | p. 55 |
Noether-Lefschetz loci in period domains | p. 61 |
The Mumford-Tate Group of a Variation of Hodge Structure | p. 67 |
The structure theorem for variations of Hodge structures | p. 69 |
An application of Mumford-Tate groups | p. 78 |
Noether-Lefschetz loci and variations of Hodge structure | p. 81 |
Hodge Representations and Hodge Domains | p. 85 |
Part I: Hodge representations | p. 86 |
The adjoint representation and characterization of which weights give faithful Hodge representations | p. 109 |
Examples: The classical groups | p. 117 |
Examples: The exceptional groups | p. 126 |
Characterization of Mumford-Tate groups | p. 132 |
Hodge domains | p. 149 |
Mumford-Tate domains as particular homogeneous complex manifolds | p. 168 |
Appendix: Notation from the structure theory of semi-simple Lie algebras | p. 179 |
Hodge Structures with Complex Multiplication | p. 187 |
Oriented number fields | p. 189 |
Hodge structures with special endomorphisms | p. 193 |
A categorical equivalence | p. 196 |
Polarization and Mumford-Tate groups | p. 198 |
An extended example | p. 202 |
Proofs of Propositions V.D.4 and V.D.5 in the Galois case | p. 209 |
Arithmetic Aspects of Mumford-Tate Domains | p. 213 |
Groups stabilizing subsets of D | p. 215 |
Decomposition of Noether-Lefschetz into Hodge orientations | p. 219 |
Weyl groups and permutations of Hodge orientations | p. 231 |
Galois groups and fields of definition | p. 234 |
Appendix: CM points in unitary Mumford-Tate domains | p. 239 |
Classification of Mumford-Tate Subdomains | p. 240 |
A general algorithm | p. 240 |
Classification of some CM-Hodge structures | p. 243 |
Determination of sub-Hodge-Lie-algebras | p. 246 |
Existence of domains of type IV(f) | p. 251 |
Characterization of domains of type IV(a) arid IV(f) | p. 253 |
Completion of the classification for weight 3 | p. 256 |
The weight 1 case | p. 260 |
Algebro-geometric examples for the Noether-Lefschetz-locus types | p. 265 |
Arithmetic of Period Maps of Geometric Origin | p. 269 |
Behavior of fields of definition under the period map-image and preimage | p. 270 |
Existence and density of CM points in motivic VHS | p. 275 |
Bibliography | p. 277 |
Index | p. 287 |
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