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We prove that the l-adic Chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of Shimura varieties of Hodge type over \bar{Q}_p, descend to classes in the l-adic cohomology of the minimal compactifications. These are invariant under the Galois group of the p-adic field above which the variety and the bundle are defined.
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Recent Developments in Line Bundle Cohomology and Applications to String Phenomenology
Vector bundle cohomology represents a key ingredient for string phenomenology, being associated with the massless spectrum arising in string compactifications on smooth compact manifolds. Although standard algorithmic techniques exist for performing cohomology calculations, they are laborious and ill-suited for scanning over large sets of string compactifications to find those most relevant to particle physics. In this article we review some recent progress in deriving closed-form expressions for line bundle cohomology and discuss some applications to string phenomenology.
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- Award ID(s):
- 2014086
- PAR ID:
- 10445605
- Editor(s):
- He, Yang-Hui; Ge, Mo-Lin; Bai, Cheng-Ming; Bao Jiakang; Hirst, Edward
- Date Published:
- Journal Name:
- Nankai Symposium on Mathematical Dialogues
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We prove that the ℓ-adic Chern classes of canonical extensions of automorphic vector bundles, over toroidal compactifications of Shimura varieties of Hodge type over ℚ¯𝑝, descend to classes in the ℓ-adic cohomology of the minimal compactifications. These are invariant under the Galois group of the 𝑝-adic field above which the variety and the bundle are defined.more » « less
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