MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Doctoral Theses
  • View Item
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Doctoral Theses
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Selmer groups as flat cohomology groups

Author(s)
Česnavičius, Kęstutis
Thumbnail
DownloadFull printable version (3.016Mb)
Other Contributors
Massachusetts Institute of Technology. Department of Mathematics.
Advisor
Bjorn Poonen.
Terms of use
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582
Metadata
Show full item record
Abstract
Given a prime number p, Bloch and Kato showed how the p Selmer group of an abelian variety A over a number field K is determined by the p-adic Tate module. In general, the pm1-Selmer group Selpmn A need not be determined by the mod pm Galois representation A[pm]; we show, however, that this is the case if p is large enough. More precisely, we exhibit a finite explicit set of rational primes E depending on K and A, such that Selpm A is determined by A[pm] for all ... In the course of the argument we describe the flat cohomology group ... of the ring of integers of K with coefficients in the pm- torsion A[pm] of the Neron model of A by local conditions for p V E, compare them with the local conditions defining Selm 2A, and prove that A[p't ] itself is determined by A[pm] for such p. Our method sharpens the relationship between Selpm A and ... which was observed by Mazur and continues to work for other isogenies 0 between abelian varieties over global fields provided that deg o is constrained appropriately. To illustrate it, we exhibit resulting explicit rank predictions for the elliptic curve 11A1 over certain families of number fields. Standard glueing techniques developed in the course of the proofs have applications to finite flat group schemes over global bases, permitting us to transfer many of the known local results to the global setting.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (pages 44-46).
 
Date issued
2014
URI
http://hdl.handle.net/1721.1/90180
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

Collections
  • Doctoral Theses

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.