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Bounding the K(p − 1)-local exotic Picard group at p > 3
- Award ID(s):
- 2239362
- PAR ID:
- 10621546
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Topology and its Applications
- ISSN:
- 0166-8641
- Page Range / eLocation ID:
- 109445
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We determine the Sato-Tate groups and prove the generalized Sato-Tate conjecture for the Jacobians of curves of the form y^2 = x^p−1 and y2 = x^{2p}−1, where p is an odd prime. Our results rely on the fact the Jacobians of these curves are nondegenerate, a fact that we prove in the paper. Furthermore, we compute moment statistics associated to the Sato-Tate groups. These moment statistics can be used to verify the equidistribution statement of the generalized Sato-Tate conjecture by comparing them to moment statistics obtained for the traces in the normalized L-polynomials of the curves.more » « less
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