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  The modularity/automorphy of Calabi-Yau varieties of CM type

Yui, N. (2017). The modularity/automorphy of Calabi-Yau varieties of CM type. In String-Math 2015: December 31, 2015-January 4, 2016, Tsinghua Sanya International Mathematics Forum, Sanya, China (pp. 265-297). Providence, RI: American Mathematical Society.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-6A0E-7 Version Permalink: https://hdl.handle.net/21.11116/0000-0004-6A1B-8
Genre: Conference Paper

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Yui_The modularity_automorphy of Calabi-Yau varieties of CM type_2017.pdf (Publisher version), 417KB
 
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Yui Noriko_E-Mail am 11.06.2019 (Correspondence), 5KB
 
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https://doi.org/10.1090/pspum/096 (Publisher version)
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 Creators:
Yui, Noriko1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: We consider Calabi–Yau varieties of dimension
d ≤ 3 defined over Q, and address the modularity/automorphy of such Calabi–Yau varieties. When the dimension of the associated Galois representations are large, e.g., >2, the problem poses a serious challenge and is out of reach in the general situations.
In this paper, I will concentrate on Calabi–Yau varieties of CM type, and establish their (motivic) modularity/automorphy. The expositions are focused on two examples: K3 surfaces with non-symplectic automorphisms, and Calabi-Yau threefolds of Borcea–Voisin type. We will briefly discuss arithmetic mirror symmetry for quite specific examples of K3 surfaces and Calabi–Yau threefolds of Borcea–Voisin type.

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Language(s): eng - English
 Dates: 2017
 Publication Status: Issued
 Pages: 33
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 Rev. Type: Peer
 Identifiers: DOI: 10.1090/pspum/096/01659
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Title: String-Math 2015
Place of Event: Sanya, China
Start-/End Date: 2015-12-31 - 2016-01-04

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Title: String-Math 2015 : December 31, 2015-January 4, 2016, Tsinghua Sanya International Mathematics Forum, Sanya, China
Source Genre: Proceedings
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Publ. Info: Providence, RI : American Mathematical Society
Pages: v, 297 S. Volume / Issue: - Sequence Number: - Start / End Page: 265 - 297 Identifier: ISBN: 978-1-4704-2951-5
DOI: 10.1090/pspum/096

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Title: Proceedings of symposia in pure mathematics
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Pages: - Volume / Issue: 96 Sequence Number: - Start / End Page: - Identifier: -