Crystalline representations and Neron models

We define and study the maximal crystalline subrepresentation functor, Crys(-), defined on p-adic Galois representations of the absolute Galois group of a finite extension K of Q(p) . In particular, we define and study the derived functors, Rⁱ Crys(-), of Crys(-). We then apply these functors to t...

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Main Author:	Marshall, Susan Hammond
Other Authors:	Kim, Minhyong
Language:	en_US
Published:	The University of Arizona. 2001
Subjects:	Mathematics.
Online Access:	http://hdl.handle.net/10150/290212

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spelling	ndltd-arizona.edu-oai-arizona.openrepository.com-10150-2902122015-10-23T05:13:43Z Crystalline representations and Neron models Marshall, Susan Hammond Kim, Minhyong Mathematics. We define and study the maximal crystalline subrepresentation functor, Crys(-), defined on p-adic Galois representations of the absolute Galois group of a finite extension K of Q(p) . In particular, we define and study the derived functors, Rⁱ Crys(-), of Crys(-). We then apply these functors to the study of Neron models of abelian varieties defined over K. We extend a formula of Grothendieck expressing the component group of a Neron model in terms of Galois cohomology. The extended formula is only valid for abelian varieties with semistable reduction defined over an unramified base. We explore the failure of the formula in the non-semistable case through the example furnished by Jacobians of Fermat curves. 2001 text Dissertation-Reproduction (electronic) http://hdl.handle.net/10150/290212 3016487 .b41936711 en_US Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. The University of Arizona.
collection	NDLTD
language	en_US
sources	NDLTD
topic	Mathematics.
spellingShingle	Mathematics. Marshall, Susan Hammond Crystalline representations and Neron models
description	We define and study the maximal crystalline subrepresentation functor, Crys(-), defined on p-adic Galois representations of the absolute Galois group of a finite extension K of Q(p) . In particular, we define and study the derived functors, Rⁱ Crys(-), of Crys(-). We then apply these functors to the study of Neron models of abelian varieties defined over K. We extend a formula of Grothendieck expressing the component group of a Neron model in terms of Galois cohomology. The extended formula is only valid for abelian varieties with semistable reduction defined over an unramified base. We explore the failure of the formula in the non-semistable case through the example furnished by Jacobians of Fermat curves.
author2	Kim, Minhyong
author_facet	Kim, Minhyong Marshall, Susan Hammond
author	Marshall, Susan Hammond
author_sort	Marshall, Susan Hammond
title	Crystalline representations and Neron models
title_short	Crystalline representations and Neron models
title_full	Crystalline representations and Neron models
title_fullStr	Crystalline representations and Neron models
title_full_unstemmed	Crystalline representations and Neron models
title_sort	crystalline representations and neron models
publisher	The University of Arizona.
publishDate	2001
url	http://hdl.handle.net/10150/290212
work_keys_str_mv	AT marshallsusanhammond crystallinerepresentationsandneronmodels
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Crystalline representations and Neron models

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