Αριθμητική γεωμετρία (Greek Wikipedia)

Analysis of information sources in references of the Wikipedia article "Αριθμητική γεωμετρία" in Greek language version.

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18wikipedia.org

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13ams.org

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1encyclopediaofmath.org

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1quantamagazine.org

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ams.org

Grothendieck, Alexander (1960). «The cohomology theory of abstract algebraic varieties». Proc. Internat. Congress Math. (Edinburgh, 1958). Cambridge University Press. σελίδες 103–118. MR 0130879.
Zariski, Oscar (2004) [1935]. Abhyankar, Shreeram S.· Lipman, Joseph· Mumford, David, επιμ. Algebraic surfaces. Classics in mathematics (second supplemented έκδοση). Berlin, New York: Springer-Verlag. ISBN 978-3-540-58658-6. MR 0469915.
Weil, André (1949). «Numbers of solutions of equations in finite fields». Bulletin of the American Mathematical Society 55 (5): 497–508. doi:10.1090/S0002-9904-1949-09219-4. ISSN 0002-9904.
MR 0029393
. Reprinted in Oeuvres Scientifiques/Collected Papers by André Weil ISBN 0-387-90330-5
Dwork, Bernard (1960). «On the rationality of the zeta function of an algebraic variety». American Journal of Mathematics (American Journal of Mathematics, Vol. 82, No. 3) 82 (3): 631–648. doi:10.2307/2372974. ISSN 0002-9327.
MR 0140494
.
Grothendieck, Alexander (1995) [1965]. «Formule de Lefschetz et rationalité des fonctions L». Séminaire Bourbaki. 9. Paris: Société Mathématique de France. σελίδες 41–55. MR 1608788.
Deligne, Pierre (1974). «La conjecture de Weil. I». Publications Mathématiques de l'IHÉS 43 (1): 273–307. doi:10.1007/BF02684373. ISSN 1618-1913.
MR 0340258
. http://www.numdam.org/item?id=PMIHES_1974__43__273_0.
Shimura, Goro (1989). «Yutaka Taniyama and his time. Very personal recollections». The Bulletin of the London Mathematical Society 21 (2): 186–196. doi:10.1112/blms/21.2.186. ISSN 0024-6093.
MR 976064
.
Mazur, Barry (1977). «Modular curves and the Eisenstein ideal». Publications Mathématiques de l'IHÉS 47 (1): 33–186. doi:10.1007/BF02684339.
MR 0488287
. http://www.numdam.org/item/PMIHES_1977__47__33_0/.
Mazur, Barry (1978). with appendix by Dorian Goldfeld. «Rational isogenies of prime degree». Inventiones Mathematicae 44 (2): 129–162. doi:10.1007/BF01390348. Bibcode: 1978InMat..44..129M.
MR 0482230
.
Merel, Loïc (1996). «Bornes pour la torsion des courbes elliptiques sur les corps de nombres» (στα γαλλικά). Inventiones Mathematica 124 (1): 437–449. doi:10.1007/s002220050059. Bibcode: 1996InMat.124..437M.
MR 1369424
.
Faltings, Gerd (1983). «Endlichkeitssätze für abelsche Varietäten über Zahlkörpern» (στα γερμανικά). Inventiones Mathematica 73 (3): 349–366. doi:10.1007/BF01388432. Bibcode: 1983InMat..73..349F.
MR 0718935
.
Faltings, Gerd (1984). «Erratum: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern» (στα γερμανικά). Inventiones Mathematica 75 (2): 381. doi:10.1007/BF01388572.
MR 0732554
.
Harris, Michael· Taylor, Richard (2001). The geometry and cohomology of some simple Shimura varieties. Annals of Mathematics Studies. 151. Princeton University Press. ISBN 978-0-691-09090-0. MR 1876802.

archive.org

Gowers, Timothy· Barrow-Green, June· Leader, Imre (2008). The Princeton companion to mathematics. Princeton University Press. σελίδες 773–774. ISBN 978-0-691-11880-2.
Serre, Jean-Pierre (1955). «Faisceaux Algebriques Coherents». The Annals of Mathematics 61 (2): 197–278. doi:10.2307/1969915. https://archive.org/details/sim_annals-of-mathematics_1955-03_61_2/page/197.

books.google.com

Zariski, Oscar (2004) [1935]. Abhyankar, Shreeram S.· Lipman, Joseph· Mumford, David, επιμ. Algebraic surfaces. Classics in mathematics (second supplemented έκδοση). Berlin, New York: Springer-Verlag. ISBN 978-3-540-58658-6. MR 0469915.
Harris, Michael· Taylor, Richard (2001). The geometry and cohomology of some simple Shimura varieties. Annals of Mathematics Studies. 151. Princeton University Press. ISBN 978-0-691-09090-0. MR 1876802.

doi.org

dx.doi.org

Weil, André (1949). «Numbers of solutions of equations in finite fields». Bulletin of the American Mathematical Society 55 (5): 497–508. doi:10.1090/S0002-9904-1949-09219-4. ISSN 0002-9904.
MR 0029393
. Reprinted in Oeuvres Scientifiques/Collected Papers by André Weil ISBN 0-387-90330-5
Serre, Jean-Pierre (1955). «Faisceaux Algebriques Coherents». The Annals of Mathematics 61 (2): 197–278. doi:10.2307/1969915. https://archive.org/details/sim_annals-of-mathematics_1955-03_61_2/page/197.
Dwork, Bernard (1960). «On the rationality of the zeta function of an algebraic variety». American Journal of Mathematics (American Journal of Mathematics, Vol. 82, No. 3) 82 (3): 631–648. doi:10.2307/2372974. ISSN 0002-9327.
MR 0140494
.
Deligne, Pierre (1974). «La conjecture de Weil. I». Publications Mathématiques de l'IHÉS 43 (1): 273–307. doi:10.1007/BF02684373. ISSN 1618-1913.
MR 0340258
. http://www.numdam.org/item?id=PMIHES_1974__43__273_0.
Shimura, Goro (1989). «Yutaka Taniyama and his time. Very personal recollections». The Bulletin of the London Mathematical Society 21 (2): 186–196. doi:10.1112/blms/21.2.186. ISSN 0024-6093.
MR 976064
.
Wiles, Andrew (1995). «Modular elliptic curves and Fermat's Last Theorem». Annals of Mathematics 141 (3): 443–551. doi:10.2307/2118559. OCLC 37032255. Αρχειοθετήθηκε από το πρωτότυπο στις 2011-05-10. https://web.archive.org/web/20110510062158/http://math.stanford.edu/%7Elekheng/flt/wiles.pdf. Ανακτήθηκε στις 2019-03-22.
Mazur, Barry (1977). «Modular curves and the Eisenstein ideal». Publications Mathématiques de l'IHÉS 47 (1): 33–186. doi:10.1007/BF02684339.
MR 0488287
. http://www.numdam.org/item/PMIHES_1977__47__33_0/.
Mazur, Barry (1978). with appendix by Dorian Goldfeld. «Rational isogenies of prime degree». Inventiones Mathematicae 44 (2): 129–162. doi:10.1007/BF01390348. Bibcode: 1978InMat..44..129M.
MR 0482230
.
Merel, Loïc (1996). «Bornes pour la torsion des courbes elliptiques sur les corps de nombres» (στα γαλλικά). Inventiones Mathematica 124 (1): 437–449. doi:10.1007/s002220050059. Bibcode: 1996InMat.124..437M.
MR 1369424
.
Faltings, Gerd (1983). «Endlichkeitssätze für abelsche Varietäten über Zahlkörpern» (στα γερμανικά). Inventiones Mathematica 73 (3): 349–366. doi:10.1007/BF01388432. Bibcode: 1983InMat..73..349F.
MR 0718935
.
Faltings, Gerd (1984). «Erratum: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern» (στα γερμανικά). Inventiones Mathematica 75 (2): 381. doi:10.1007/BF01388572.
MR 0732554
.

encyclopediaofmath.org

«Diophantine geometry - Encyclopedia of Mathematics». encyclopediaofmath.org. Ανακτήθηκε στις 11 Απριλίου 2024.

grothendieckcircle.org

Grothendieck, Alexander (1960). «The cohomology theory of abstract algebraic varieties». Proc. Internat. Congress Math. (Edinburgh, 1958). Cambridge University Press. σελίδες 103–118. MR 0130879.

harvard.edu

adsabs.harvard.edu

Mazur, Barry (1978). with appendix by Dorian Goldfeld. «Rational isogenies of prime degree». Inventiones Mathematicae 44 (2): 129–162. doi:10.1007/BF01390348. Bibcode: 1978InMat..44..129M.
MR 0482230
.
Merel, Loïc (1996). «Bornes pour la torsion des courbes elliptiques sur les corps de nombres» (στα γαλλικά). Inventiones Mathematica 124 (1): 437–449. doi:10.1007/s002220050059. Bibcode: 1996InMat.124..437M.
MR 1369424
.
Faltings, Gerd (1983). «Endlichkeitssätze für abelsche Varietäten über Zahlkörpern» (στα γερμανικά). Inventiones Mathematica 73 (3): 349–366. doi:10.1007/BF01388432. Bibcode: 1983InMat..73..349F.
MR 0718935
.

mathunion.org

«Fields Medals 2018». International Mathematical Union. Ανακτήθηκε στις 2 Αυγούστου 2018.

mit.edu

ocw.mit.edu

Sutherland, Andrew V. (5 Σεπτεμβρίου 2013). «Introduction to Arithmetic Geometry» (PDF). Ανακτήθηκε στις 22 Μαρτίου 2019.

math.mit.edu

Poonen, Bjorn (2009). «Introduction to Arithmetic Geometry» (PDF). Ανακτήθηκε στις 22 Μαρτίου 2019.

ncatlab.org

«arithmetic geometry in nLab». ncatlab.org. Ανακτήθηκε στις 11 Απριλίου 2024.

numdam.org

Grothendieck, Alexander (1995) [1965]. «Formule de Lefschetz et rationalité des fonctions L». Séminaire Bourbaki. 9. Paris: Société Mathématique de France. σελίδες 41–55. MR 1608788.
Deligne, Pierre (1974). «La conjecture de Weil. I». Publications Mathématiques de l'IHÉS 43 (1): 273–307. doi:10.1007/BF02684373. ISSN 1618-1913.
MR 0340258
. http://www.numdam.org/item?id=PMIHES_1974__43__273_0.
Mazur, Barry (1977). «Modular curves and the Eisenstein ideal». Publications Mathématiques de l'IHÉS 47 (1): 33–186. doi:10.1007/BF02684339.
MR 0488287
. http://www.numdam.org/item/PMIHES_1977__47__33_0/.

quantamagazine.org

Klarreich, Erica (28 Ιουνίου 2016). «Peter Scholze and the Future of Arithmetic Geometry». Ανακτήθηκε στις 22 Μαρτίου 2019.

stanford.edu

math.stanford.edu

Wiles, Andrew (1995). «Modular elliptic curves and Fermat's Last Theorem». Annals of Mathematics 141 (3): 443–551. doi:10.2307/2118559. OCLC 37032255. Αρχειοθετήθηκε από το πρωτότυπο στις 2011-05-10. https://web.archive.org/web/20110510062158/http://math.stanford.edu/%7Elekheng/flt/wiles.pdf. Ανακτήθηκε στις 2019-03-22.

ubc.ca

sunsite.ubc.ca

Langlands, Robert (1979). «Automorphic Representations, Shimura Varieties, and Motives. Ein Märchen» (PDF). Στο: Borel, Armand· Casselman, William. Automorphic Forms, Representations, and L-Functions: Symposium in Pure Mathematics. XXXIII Part 1. Chelsea Publishing Company. σελίδες 205–246.

uni-bonn.de

math.uni-bonn.de

Scholze, Peter. «Perfectoid spaces: A survey» (PDF). University of Bonn. Ανακτήθηκε στις 4 Νοεμβρίου 2018.

web.archive.org

Wiles, Andrew (1995). «Modular elliptic curves and Fermat's Last Theorem». Annals of Mathematics 141 (3): 443–551. doi:10.2307/2118559. OCLC 37032255. Αρχειοθετήθηκε από το πρωτότυπο στις 2011-05-10. https://web.archive.org/web/20110510062158/http://math.stanford.edu/%7Elekheng/flt/wiles.pdf. Ανακτήθηκε στις 2019-03-22.

wikipedia.org

en.wikipedia.org

Poonen, Bjorn (2009). «Introduction to Arithmetic Geometry» (PDF). Ανακτήθηκε στις 22 Μαρτίου 2019.
Lang, Serge (1997). Survey of Diophantine Geometry. Springer-Verlag. σελίδες 43–67. ISBN 3-540-61223-8. Zbl 0869.11051.
Grothendieck, Alexander (1960). «The cohomology theory of abstract algebraic varieties». Proc. Internat. Congress Math. (Edinburgh, 1958). Cambridge University Press. σελίδες 103–118. MR 0130879.
Serre, Jean-Pierre (1967). «Résumé des cours, 1965–66». Annuaire du Collège de France (Paris): 49–58.
Mordell, Louis J. (1969). Diophantine Equations. Academic Press. σελ. 1. ISBN 978-0125062503.
Zariski, Oscar (2004) [1935]. Abhyankar, Shreeram S.· Lipman, Joseph· Mumford, David, επιμ. Algebraic surfaces. Classics in mathematics (second supplemented έκδοση). Berlin, New York: Springer-Verlag. ISBN 978-3-540-58658-6. MR 0469915.
Weil, André (1949). «Numbers of solutions of equations in finite fields». Bulletin of the American Mathematical Society 55 (5): 497–508. doi:10.1090/S0002-9904-1949-09219-4. ISSN 0002-9904.
MR 0029393
. Reprinted in Oeuvres Scientifiques/Collected Papers by André Weil ISBN 0-387-90330-5
Dwork, Bernard (1960). «On the rationality of the zeta function of an algebraic variety». American Journal of Mathematics (American Journal of Mathematics, Vol. 82, No. 3) 82 (3): 631–648. doi:10.2307/2372974. ISSN 0002-9327.
MR 0140494
.
Grothendieck, Alexander (1995) [1965]. «Formule de Lefschetz et rationalité des fonctions L». Séminaire Bourbaki. 9. Paris: Société Mathématique de France. σελίδες 41–55. MR 1608788.
Deligne, Pierre (1974). «La conjecture de Weil. I». Publications Mathématiques de l'IHÉS 43 (1): 273–307. doi:10.1007/BF02684373. ISSN 1618-1913.
MR 0340258
. http://www.numdam.org/item?id=PMIHES_1974__43__273_0.
Langlands, Robert (1979). «Automorphic Representations, Shimura Varieties, and Motives. Ein Märchen» (PDF). Στο: Borel, Armand· Casselman, William. Automorphic Forms, Representations, and L-Functions: Symposium in Pure Mathematics. XXXIII Part 1. Chelsea Publishing Company. σελίδες 205–246.
Mazur, Barry (1977). «Modular curves and the Eisenstein ideal». Publications Mathématiques de l'IHÉS 47 (1): 33–186. doi:10.1007/BF02684339.
MR 0488287
. http://www.numdam.org/item/PMIHES_1977__47__33_0/.
Mazur, Barry (1978). with appendix by Dorian Goldfeld. «Rational isogenies of prime degree». Inventiones Mathematicae 44 (2): 129–162. doi:10.1007/BF01390348. Bibcode: 1978InMat..44..129M.
MR 0482230
.
Merel, Loïc (1996). «Bornes pour la torsion des courbes elliptiques sur les corps de nombres» (στα γαλλικά). Inventiones Mathematica 124 (1): 437–449. doi:10.1007/s002220050059. Bibcode: 1996InMat.124..437M.
MR 1369424
.
Faltings, Gerd (1983). «Endlichkeitssätze für abelsche Varietäten über Zahlkörpern» (στα γερμανικά). Inventiones Mathematica 73 (3): 349–366. doi:10.1007/BF01388432. Bibcode: 1983InMat..73..349F.
MR 0718935
.
Faltings, Gerd (1984). «Erratum: Endlichkeitssätze für abelsche Varietäten über Zahlkörpern» (στα γερμανικά). Inventiones Mathematica 75 (2): 381. doi:10.1007/BF01388572.
MR 0732554
.
Harris, Michael· Taylor, Richard (2001). The geometry and cohomology of some simple Shimura varieties. Annals of Mathematics Studies. 151. Princeton University Press. ISBN 978-0-691-09090-0. MR 1876802.
«Fields Medals 2018». International Mathematical Union. Ανακτήθηκε στις 2 Αυγούστου 2018.

worldcat.org

Weil, André (1949). «Numbers of solutions of equations in finite fields». Bulletin of the American Mathematical Society 55 (5): 497–508. doi:10.1090/S0002-9904-1949-09219-4. ISSN 0002-9904.
MR 0029393
. Reprinted in Oeuvres Scientifiques/Collected Papers by André Weil ISBN 0-387-90330-5
Dwork, Bernard (1960). «On the rationality of the zeta function of an algebraic variety». American Journal of Mathematics (American Journal of Mathematics, Vol. 82, No. 3) 82 (3): 631–648. doi:10.2307/2372974. ISSN 0002-9327.
MR 0140494
.
Deligne, Pierre (1974). «La conjecture de Weil. I». Publications Mathématiques de l'IHÉS 43 (1): 273–307. doi:10.1007/BF02684373. ISSN 1618-1913.
MR 0340258
. http://www.numdam.org/item?id=PMIHES_1974__43__273_0.
Shimura, Goro (1989). «Yutaka Taniyama and his time. Very personal recollections». The Bulletin of the London Mathematical Society 21 (2): 186–196. doi:10.1112/blms/21.2.186. ISSN 0024-6093.
MR 976064
.
Wiles, Andrew (1995). «Modular elliptic curves and Fermat's Last Theorem». Annals of Mathematics 141 (3): 443–551. doi:10.2307/2118559. OCLC 37032255. Αρχειοθετήθηκε από το πρωτότυπο στις 2011-05-10. https://web.archive.org/web/20110510062158/http://math.stanford.edu/%7Elekheng/flt/wiles.pdf. Ανακτήθηκε στις 2019-03-22.

zbmath.org

Lang, Serge (1997). Survey of Diophantine Geometry. Springer-Verlag. σελίδες 43–67. ISBN 3-540-61223-8. Zbl 0869.11051.