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Abstract We construct an Euler system associated to regular algebraic, essentially conjugate self-dual cuspidal automorphic representations of $${{\,\mathrm{GL}\,}}_3$$ GL 3 over imaginary quadratic fields, using the cohomology of Shimura varieties for $${\text {GU}}(2, 1)$$ GU ( 2 , 1 ) .
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Odd-Dimensional GKM-Manifolds of Non-Negative Curvature
Abstract Let $$M$$ be a closed, odd GKM$$_3$$ manifold of non-negative sectional curvature. We show that in this situation one can associate an ordinary abstract GKM$$_3$$ graph to $$M$$ and prove that if this graph is orientable, then both the equivariant and the ordinary rational cohomology of $$M$$ split off the cohomology of an odd-dimensional sphere.
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- Award ID(s):
- 1906404
- PAR ID:
- 10439522
- Date Published:
- Journal Name:
- International Mathematics Research Notices
- Volume:
- 2023
- Issue:
- 1
- ISSN:
- 1073-7928
- Page Range / eLocation ID:
- 744 to 784
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1093/imrn/rnab137
