Grothendieck's pairing on Neron component groups /

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Bibliographic Details
Author / Creator:	Suzuki, Takashi, author.
Imprint:	2015. Ann Arbor : ProQuest Dissertations & Theses, 2015
Description:	1 electronic resource (61 pages)
Language:	English
Format:	E-Resource Dissertations
Local Note:	School code: 0330
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/10773189

Hidden Bibliographic Details
Other authors / contributors:	University of Chicago. degree granting institution.
ISBN:	9781321918434
Notes:	Advisors: Kazuya Kato Committee members: Takako Fukaya. This item must not be sold to any third party vendors. Dissertation Abstracts International, Volume: 76-12(E), Section: B. English
Summary:	In this thesis, we construct a duality theory for a complete discrete valuation field K with perfect residue field. The main results are improvement of Serre's class field theory for K and, as an application, solution to a conjecture of Grothendieck on the special fibers of abelian varieties over K. The key is to introduce a new Grothendieck site. This makes Serre's theory completely functorial in the derived category of sheaves. We apply this new framework to abelian varieties, with which we can deduce the general case of Grothendieck's conjecture by Galois descent from the known case of semistable abelian varieties.

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