{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:57:48Z","timestamp":1780387068522,"version":"3.54.1"},"reference-count":31,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2001,9,1]],"date-time":"2001-09-01T00:00:00Z","timestamp":999302400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":4337,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Annals of Pure and Applied Logic"],"published-print":{"date-parts":[[2001,9]]},"DOI":"10.1016\/s0168-0072(01)00096-3","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T20:20:37Z","timestamp":1027628437000},"page":"43-115","source":"Crossref","is-referenced-by-count":62,"title":["The Manin\u2013Mumford conjecture and the model theory of difference fields"],"prefix":"10.1016","volume":"112","author":[{"given":"Ehud","family":"Hrushovski","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/S0168-0072(01)00096-3_BIB1","unstructured":"J.-B. Bost, P\u00e9riodes et isogenies des vari\u00e9t\u00e9s ab\u00e9liennes sur les corps de nombres, d'apres D. Masser et G. W\u00fcstholz. S\u00e9minarie Bourbaki Exp. No. 795."},{"issue":"2","key":"10.1016\/S0168-0072(01)00096-3_BIB2","doi-asserted-by":"crossref","first-page":"579","DOI":"10.2307\/2275409","article-title":"On one-based theories","volume":"59","author":"Bouscaren","year":"1994","journal-title":"J. Symbolic Logic"},{"issue":"1","key":"10.1016\/S0168-0072(01)00096-3_BIB3","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0168-0072(86)90038-2","article-title":"Locally modular theories of finite rank","volume":"30","author":"Buechler","year":"1986","journal-title":"Ann. Pure Appl. Logic"},{"issue":"2","key":"10.1016\/S0168-0072(01)00096-3_BIB4","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1215\/S0012-7094-96-08216-2","article-title":"Geometry of p-adic jets","volume":"82","author":"Buium","year":"1996","journal-title":"Duke J. Math"},{"issue":"8","key":"10.1016\/S0168-0072(01)00096-3_BIB5","doi-asserted-by":"crossref","first-page":"2997","DOI":"10.1090\/S0002-9947-99-02498-8","article-title":"Model theory of difference fields","volume":"351","author":"Chatzidakis","year":"2000","journal-title":"AMS Trans."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB6","doi-asserted-by":"crossref","unstructured":"Z. Chatzidakis, E. Hrushovski, Y. Peterzil, Model Theory of difference fields II: periodic ideals and the trichotomy in all characteristics, Trans. AMS, to appear.","DOI":"10.1112\/S0024611502013576"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB7","series-title":"Model Theory","author":"Chang","year":"1990"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB8","unstructured":"G. Cherlin, E. Hrushovski, Quasi-finite structures (preprint available in www.math.rutgers.edu\/\/cherlin)."},{"issue":"3","key":"10.1016\/S0168-0072(01)00096-3_BIB9","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF01388432","article-title":"Endlichkeitss\u00e4tze f\u00fcr abelsche Variet\u00e4ten \u00fcber Zahlk\u00f6rpern","volume":"73","author":"Faltings","year":"1983","journal-title":"Invent. Math."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB10","series-title":"Intersection Theory","author":"Fulton","year":"1984"},{"issue":"3","key":"10.1016\/S0168-0072(01)00096-3_BIB11","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/BF01394276","article-title":"Autour d'une conjecture de Serge Lang","volume":"94","author":"Hindry","year":"1988","journal-title":"Invent. Math."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB12","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0168-0072(90)90046-5","article-title":"Unidimensional theories are superstable","volume":"50","author":"Hrushovski","year":"1990","journal-title":"Ann. Pure Appl. Logic"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB13","unstructured":"E. Hrushovski, The Manin\u2013Mumford conjecture and the model theory of difference fields, extended abstract (5pp), in: M. Jarden (Ed.), Proc. Field Arithmetic conf., Institute for Advanced Study, Jerusalem, 1995."},{"issue":"3","key":"10.1016\/S0168-0072(01)00096-3_BIB14","first-page":"667","article-title":"The Mordell\u2013Lang conjecture for function fields","volume":"9","author":"Hrushovski","year":"1996","journal-title":"J. AMS"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB15","doi-asserted-by":"crossref","unstructured":"E. Hrushovski, A. Pillay, Weakly normal groups, in: Logic Colloquium 85, North-Holland, Amsterdam, 1986.","DOI":"10.1016\/S0049-237X(09)70556-7"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB16","first-page":"69","article-title":"Definable subgroups of algebraic groups over finite fields","volume":"462","author":"Hrushovski","year":"1995","journal-title":"J. Reine Angew. Math."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB17","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0168-0072(97)00019-5","article-title":"Simple theories","volume":"88","author":"Kim","year":"1997","journal-title":"Ann. Pure Appl. Logic"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB18","doi-asserted-by":"crossref","unstructured":"S. Lang, in: Number Theory III: Diophantine Geometry, Encyclopaedia of Mathematical Sciences, Vol. 60, Springer, Berlin, Heidelberg, 1991.","DOI":"10.1007\/978-3-642-58227-1"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB19","doi-asserted-by":"crossref","first-page":"659","DOI":"10.2307\/2372778","article-title":"Principal homogeneous spaces over abelian varieties","volume":"80","author":"Lang","year":"1958","journal-title":"Amer. J. Math."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB20","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF02699374","article-title":"Factorisation estimates for abelian varieties","volume":"81","author":"Masser","year":"1995","journal-title":"Pub. Math. IHES"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB21","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/BF01241125","article-title":"Division points on semi-abelian varieties","volume":"120","author":"McQuillan","year":"1995","journal-title":"Invent. Math."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB22","unstructured":"A. Pillay, Model theory, stability theory, and stable groups, in: A. Nesin, A. Pillay (Eds.), The Model Theory of Groups, Notre Dame Mathematical Lectures 11, University of Notre Dame Press, Notre Dame, Indiana, 1989."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB23","unstructured":"M. Raynaud, Around the Mordell conjecture for function fields and a conjecture of Serge Lang, in: Proc. Algebraic Geometry of Tokyo, Lecture Notes, vol. 1016, Springer, Berlin, 1982."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB24","series-title":"Introduction to Model Theory and the Metamathematics of Algebra","author":"Robinson","year":"1963"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB25","series-title":"Saturated Model Theory","author":"Sacks","year":"1972"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB26","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1515\/crll.1998.060","article-title":"Conjecture of Tate and Voloch on p-adic proximity to torsion, International Math. Research Notices 1999 no 17, 909\u2013914; p-adic distance from torsion points of semi-Abelian varieties","volume":"499","author":"Scanlon","year":"1998","journal-title":"J. Reine Angew. Math."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB27","series-title":"Lectures on the Mordell\u2013Weil Theorem","author":"Serre","year":"1997"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB28","volume":"Vol. 1264","author":"Serre","year":"1959"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB29","unstructured":"J.-P. Serre, Oeuvres, Vol. IV, 1985\u20131998, Springer, Berlin, 2000."},{"key":"10.1016\/S0168-0072(01)00096-3_BIB30","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0003-4843(80)90009-1","article-title":"Simple unstable theories","volume":"19","author":"Shelah","year":"1980","journal-title":"Ann. Math. Logic"},{"key":"10.1016\/S0168-0072(01)00096-3_BIB31","series-title":"Vari\u00e9t\u00e9s abeliennes et courbes alg\u00e9briques","author":"Weil","year":"1948"}],"container-title":["Annals of Pure and Applied Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0168007201000963?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0168007201000963?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T06:09:32Z","timestamp":1579154972000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0168007201000963"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,9]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2001,9]]}},"alternative-id":["S0168007201000963"],"URL":"https:\/\/doi.org\/10.1016\/s0168-0072(01)00096-3","relation":{},"ISSN":["0168-0072"],"issn-type":[{"value":"0168-0072","type":"print"}],"subject":[],"published":{"date-parts":[[2001,9]]}}}