Faltings's theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Faltings's theorem" in English language version.

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Faltings 1983; Faltings 1984. Faltings, Gerd (1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae (in German). 73 (3): 349–366. Bibcode:1983InMat..73..349F. doi:10.1007/BF01388432. MR 0718935. Faltings, Gerd (1984). "Erratum: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern". Inventiones Mathematicae (in German). 75 (2): 381. doi:10.1007/BF01388572. MR 0732554.
Faltings 1983. Faltings, Gerd (1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae (in German). 73 (3): 349–366. Bibcode:1983InMat..73..349F. doi:10.1007/BF01388432. MR 0718935.
Vojta 1991. Vojta, Paul (1991). "Siegel's theorem in the compact case". Ann. of Math. 133 (3): 509–548. doi:10.2307/2944318. JSTOR 2944318. MR 1109352.
Bombieri 1990. Bombieri, Enrico (1990). "The Mordell conjecture revisited". Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (4): 615–640. MR 1093712.
Manin 1963. Manin, Ju. I. (1963). "Rational points on algebraic curves over function fields". Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya (in Russian). 27: 1395–1440. ISSN 0373-2436. MR 0157971. (Translation: Manin, Yu. (1966). "Rational points on algebraic curves over function fields". American Mathematical Society Translations. Series 2. 59: 189–234. doi:10.1090/trans2/050/11. ISBN 9780821817506. ISSN 0065-9290. )
Grauert 1965. Grauert, Hans (1965). "Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper". Publications Mathématiques de l'IHÉS. 25 (25): 131–149. doi:10.1007/BF02684399. ISSN 1618-1913. MR 0222087.
Coleman 1990. Coleman, Robert F. (1990). "Manin's proof of the Mordell conjecture over function fields". L'Enseignement Mathématique. 2e Série. 36 (3): 393–427. ISSN 0013-8584. MR 1096426.

archive.org

Mordell 1922. Mordell, Louis J. (1922). "On the rational solutions of the indeterminate equation of the third and fourth degrees". Proc. Cambridge Philos. Soc. 21: 179–192.

arxiv.org

Lawrence & Venkatesh 2020. Lawrence, Brian; Venkatesh, Akshay (2020). "Diophantine problems and $p$ -adic period mappings". Invent. Math. 221 (3): 893–999. arXiv:1807.02721. Bibcode:2020InMat.221..893L. doi:10.1007/s00222-020-00966-7.

doi.org

"Faltings relates the two notions of height by means of the Siegel moduli space.... It is the main idea of the proof." Bloch, Spencer (1984). "The Proof of the Mordell Conjecture". The Mathematical Intelligencer. 6 (2): 44. doi:10.1007/BF03024155. S2CID 306251.
Faltings 1983; Faltings 1984. Faltings, Gerd (1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae (in German). 73 (3): 349–366. Bibcode:1983InMat..73..349F. doi:10.1007/BF01388432. MR 0718935. Faltings, Gerd (1984). "Erratum: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern". Inventiones Mathematicae (in German). 75 (2): 381. doi:10.1007/BF01388572. MR 0732554.
Parshin 1968. Parshin, A. N. (1968). "Algebraic curves over function fields I". Izv. Akad. Nauk SSSR Ser. Mat. 32 (5): 1191–1219. Bibcode:1968IzMat...2.1145P. doi:10.1070/IM1968v002n05ABEH000723.
Faltings 1983. Faltings, Gerd (1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae (in German). 73 (3): 349–366. Bibcode:1983InMat..73..349F. doi:10.1007/BF01388432. MR 0718935.
Vojta 1991. Vojta, Paul (1991). "Siegel's theorem in the compact case". Ann. of Math. 133 (3): 509–548. doi:10.2307/2944318. JSTOR 2944318. MR 1109352.
Lawrence & Venkatesh 2020. Lawrence, Brian; Venkatesh, Akshay (2020). "Diophantine problems and $p$ -adic period mappings". Invent. Math. 221 (3): 893–999. arXiv:1807.02721. Bibcode:2020InMat.221..893L. doi:10.1007/s00222-020-00966-7.
McQuillan 1995. McQuillan, Michael (1995). "Division points on semi-abelian varieties". Invent. Math. 120 (1): 143–159. Bibcode:1995InMat.120..143M. doi:10.1007/BF01241125.
Manin 1963. Manin, Ju. I. (1963). "Rational points on algebraic curves over function fields". Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya (in Russian). 27: 1395–1440. ISSN 0373-2436. MR 0157971. (Translation: Manin, Yu. (1966). "Rational points on algebraic curves over function fields". American Mathematical Society Translations. Series 2. 59: 189–234. doi:10.1090/trans2/050/11. ISBN 9780821817506. ISSN 0065-9290. )
Grauert 1965. Grauert, Hans (1965). "Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper". Publications Mathématiques de l'IHÉS. 25 (25): 131–149. doi:10.1007/BF02684399. ISSN 1618-1913. MR 0222087.

e-periodica.ch

Coleman 1990. Coleman, Robert F. (1990). "Manin's proof of the Mordell conjecture over function fields". L'Enseignement Mathématique. 2e Série. 36 (3): 393–427. ISSN 0013-8584. MR 1096426.

harvard.edu

ui.adsabs.harvard.edu

Faltings 1983; Faltings 1984. Faltings, Gerd (1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae (in German). 73 (3): 349–366. Bibcode:1983InMat..73..349F. doi:10.1007/BF01388432. MR 0718935. Faltings, Gerd (1984). "Erratum: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern". Inventiones Mathematicae (in German). 75 (2): 381. doi:10.1007/BF01388572. MR 0732554.
Parshin 1968. Parshin, A. N. (1968). "Algebraic curves over function fields I". Izv. Akad. Nauk SSSR Ser. Mat. 32 (5): 1191–1219. Bibcode:1968IzMat...2.1145P. doi:10.1070/IM1968v002n05ABEH000723.
Faltings 1983. Faltings, Gerd (1983). "Endlichkeitssätze für abelsche Varietäten über Zahlkörpern" [Finiteness theorems for abelian varieties over number fields]. Inventiones Mathematicae (in German). 73 (3): 349–366. Bibcode:1983InMat..73..349F. doi:10.1007/BF01388432. MR 0718935.
Lawrence & Venkatesh 2020. Lawrence, Brian; Venkatesh, Akshay (2020). "Diophantine problems and $p$ -adic period mappings". Invent. Math. 221 (3): 893–999. arXiv:1807.02721. Bibcode:2020InMat.221..893L. doi:10.1007/s00222-020-00966-7.
McQuillan 1995. McQuillan, Michael (1995). "Division points on semi-abelian varieties". Invent. Math. 120 (1): 143–159. Bibcode:1995InMat.120..143M. doi:10.1007/BF01241125.

jstor.org

Vojta 1991. Vojta, Paul (1991). "Siegel's theorem in the compact case". Ann. of Math. 133 (3): 509–548. doi:10.2307/2944318. JSTOR 2944318. MR 1109352.

mathnet.ru

mi.mathnet.ru

Manin 1963. Manin, Ju. I. (1963). "Rational points on algebraic curves over function fields". Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya (in Russian). 27: 1395–1440. ISSN 0373-2436. MR 0157971. (Translation: Manin, Yu. (1966). "Rational points on algebraic curves over function fields". American Mathematical Society Translations. Series 2. 59: 189–234. doi:10.1090/trans2/050/11. ISBN 9780821817506. ISSN 0065-9290. )

numdam.org

Bombieri 1990. Bombieri, Enrico (1990). "The Mordell conjecture revisited". Ann. Scuola Norm. Sup. Pisa Cl. Sci. 17 (4): 615–640. MR 1093712.
Grauert 1965. Grauert, Hans (1965). "Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper". Publications Mathématiques de l'IHÉS. 25 (25): 131–149. doi:10.1007/BF02684399. ISSN 1618-1913. MR 0222087.

semanticscholar.org

api.semanticscholar.org

"Faltings relates the two notions of height by means of the Siegel moduli space.... It is the main idea of the proof." Bloch, Spencer (1984). "The Proof of the Mordell Conjecture". The Mathematical Intelligencer. 6 (2): 44. doi:10.1007/BF03024155. S2CID 306251.

worldcat.org

search.worldcat.org

Manin 1963. Manin, Ju. I. (1963). "Rational points on algebraic curves over function fields". Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya (in Russian). 27: 1395–1440. ISSN 0373-2436. MR 0157971. (Translation: Manin, Yu. (1966). "Rational points on algebraic curves over function fields". American Mathematical Society Translations. Series 2. 59: 189–234. doi:10.1090/trans2/050/11. ISBN 9780821817506. ISSN 0065-9290. )
Grauert 1965. Grauert, Hans (1965). "Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper". Publications Mathématiques de l'IHÉS. 25 (25): 131–149. doi:10.1007/BF02684399. ISSN 1618-1913. MR 0222087.
Coleman 1990. Coleman, Robert F. (1990). "Manin's proof of the Mordell conjecture over function fields". L'Enseignement Mathématique. 2e Série. 36 (3): 393–427. ISSN 0013-8584. MR 1096426.