Fetching the paper…
Reading the bibliography…
Tropicalizations form a bridge between algebraic and convex geometry.
A. Grothendieck, J. Dieudonné: Éléments de géometrie algébrique. I: Le langage des schémas. Publ. Math. IHES 4, 5–228 (1960)
1960
Earlier work this paper cites.
A. Grothendieck, J. Dieudonné: Éléments de géometrie algébrique. II: Étude globale élémentaire de quelques classes de morphismes. Publ. Math. IHES 8, 1–222 (1961)
1961
Earlier work this paper cites.
A. Grothendieck: Fondements de la Géométrie Algébrique. Séminaire Bourbaki 1957–1962. Secrétariat Math., Paris (1962)
1962
Earlier work this paper cites.
A. Grothendieck, J. Dieudonné: Éléments de géometrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. Publ. Math. IHES 20 (1964), 24 (1965), 28 (1966), 32 (1967)
1967
Earlier work this paper cites.
R. T. Rockafellar: Convex analysis. Princeton, N. J.: Princeton University Press (1970)
1970
Earlier work this paper cites.
G.M. Bergman: The logarithmic limit-set of an algebraic variety. Trans. Am. Math. Soc. 157, 459–470 (1971)
1971
Earlier work this paper cites.
M. Raynaud, L. Gruson: Critères de platitude et de projectivité. Invent. Math. 13, 1–89 (1971)
1971
Earlier work this paper cites.
G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat: Toroidal embeddings. I. LNM 339. Berlin etc.: Springer-Verlag (1973)
1973
Earlier work this paper cites.
R. Hartshorne: Algebraic geometry. GTM 52, Springer, Berlin, Heidelberg, New York (1977)
1977
Earlier work this paper cites.
A.B. Altman, S.L. Kleiman: Compactifying the Picard scheme. Adv. Math. 35, 50–112 (1980)
1980
Earlier work this paper cites.
R. Bieri, J.R.J. Groves: The geometry of the set of characters induced by valuations. J. Reine Angew. Math. 347, 168-195 (1984)
1984
Earlier work this paper cites.
S. Bosch, U. Güntzer, R. Remmert: Non-Archimedean analysis. A systematic approach to rigid analytic geometry. Grundl. Math. Wiss., 261. Berlin etc.: Springer Verlag (1984)
1984
Earlier work this paper cites.
W. Fulton: Intersection theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, Bd. 2. Springer, Berlin etc. (1984)
1984
Earlier work this paper cites.
T. Oda: Convex bodies and algebraic geometry. An introduction to the theory of toric varieties. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, Bd. 15. Berlin etc.: Springer-Verlag. viii, 212 p. (1988)
1988
Earlier work this paper cites.
N. Bourbaki: Elements of Mathematics: Commutative Algebra. Chapters 1–7. Softcover edition of the 2nd printing. Berlin: Springer (1989)
1989
Earlier work this paper cites.
V.G. Berkovich: Spectral theory and analytic geometry over non-archimedean fields. Mathematical Surveys and Monographs, 33. Providence, RI: AMS (1990)
1990
Earlier work this paper cites.
A. Borel: Linear algebraic groups. 2nd enl. edition. GTM 126, Springer (1990)
1990
Earlier work this paper cites.
S. Bosch, W. Lütkebohmert, M. Raynaud: Néron models. Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, 21. Springer, Berlin etc. (1990)
1990
Cited alongside, same era.
V.G. Berkovich: Étale cohomology for non-archimedean analytic spaces. Publ. Math. IHES 78, 5–161 (1993)
1993
Cited alongside, same era.
S. Bosch, W. Lütkebohmert: Formal and rigid geometry. I: Rigid spaces. Math. Ann. 295, No.2, 291–317 (1993)
1993
Cited alongside, same era.
W. Fulton: Introduction to toric varieties. The 1989 W. H. Roever lectures in geometry. Annals of Math. Studies, 131. Princeton, NJ: Princeton University Press (1993)
1993
Cited alongside, same era.
D. Mumford, J. Fogarty, F. Kirwan: Geometric invariant theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. 34. Springer, Berlin (1993)
1993
Cited alongside, same era.
M. Einsiedler, M. Kapranov, D. Lind: Non-archimedean amoebas and tropical varieties. J. Reine Angew. Math. 601, 139–157 (2006)
2006
Later among the works it cites.
G. Mikhalkin: Tropical geometry and its applications. Sanz-Solé, Marta (ed.) et al., Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume II: Invited lectures. Zürich: European Mathematical Society (EMS). 827-852 (2006)
2006
Later among the works it cites.
W. Gubler: Tropical varieties for non-archimedean analytic spaces. Invent. Math. 169, No.2, 321–376 (2007)
2007
Later among the works it cites.
G.L. Litvinov: The Maslov dequantization, idempotent and tropical mathematics: a brief introduction. Zap. Nauchn. Semin. POMI 326, 145–182 (2005); translation in J. Math. Sci., New York 140, No. 3, 426–444 (2007)
2007
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
B. Poonen: Maximally complete fields. Enseign. Math., II. Sér. 39, No.1-2, 87–106 (1993)
1993
Cited alongside, same era.
I. Gelfand, M. Kapranov, A. Zelevinsky: Discriminants, resultants, and multidimensional determinants. Birkhäuser (1994)
1994
Cited alongside, same era.
P. Ullrich: The direct image theorem in formal and rigid geometry. Math. Ann. 301, No.1, 69–104 (1995)
1995
Cited alongside, same era.
W. Fulton, Sturmfels: Intersection theory on toric varieties. Topology 36, No.2, 335–353 (1997)
1997
Cited alongside, same era.
A. L. Smirnov: Torus schemes over a discrete valuation ring. (Russian. Russian summary) Algebra i Analiz 8 (1996), no. 4, 161–172; translation in St. Petersburg Math. J. 8, no. 4, 651659 (1997)
1997
Cited alongside, same era.
W. Gubler: Local heights of subvarieties over non-archimedean fields, J. reine angew. Math. 498, 61-113 (1998)
1998
Cited alongside, same era.
B. Sturmfels: Solving systems of polynomial equations, CBMS Regional Conference Series in Mathematics 97. Amer. Math. Soc. (2002)
2002
Cited alongside, same era.
2007
Later among the works it cites.
J. Draisma: A tropical approach to secant dimensions. J. Pure Appl. Algebra 212, No. 2, 349-363 (2008)
2008
Later among the works it cites.
B. Sturmfels, J. Tevelev: Elimination theory for tropical varieties. Math. Res. Lett. 15, No. 2-3, 543–562 (2008)
2008
Later among the works it cites.
A. Ducros: Les espaces de Berkovich sont excellents. Ann. Inst. Fourier 59, No.4, 1407–1516 (2009)
2009
Later among the works it cites.
E. Katz: A tropical toolkit. Expo. Math. 27, No. 1, 1-36 (2009)
2009
Later among the works it cites.
D. Maclagan, B. Sturmfels: Introduction to tropical geometry. Preliminary draft (4.11.2009)
2009
Later among the works it cites.
S. Payne: Analytification is the limit of all tropicalizations. Math. Res. Lett. 16, 543–556 (2009)
2009
Later among the works it cites.
Z. Qu: Toric schemes over a discrete valuation ring and tropical compactifications. Ph.D. thesis, University of Texas at Austin (2009)
2009
Later among the works it cites.
R. Wilke: Totally degenerated formal schemes. PhD thesis in Ulm (2009)
2009
Later among the works it cites.
L. Allermann, J. Rau: First steps in tropical intersection theory. Math. Z. 264, No. 3, 633-670 (2010)
2010
Later among the works it cites.
D. A. Cox, J. B. Little, H. Schenk: Toric varieties. Graduate Studies in Mathematics, 124: AMS (2011)
2011
Closest in time.
J. Rabinoff: Tropical analytic geometry, Newton polygons, and tropical intersections. Adv. Math. 229, No. 6, 3192–3255 (2012)
2012
Closest in time.