Non-archimedean amoebas and tropical varieties

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 601, 2006, Pages 139-157

  Einsiedler, Manfred ^a,b   Kapranov, Mikhail ^a,c   Lind, Douglas ^a,b  

^a University of Washington ^*

^b UNIVERSITY OF WASHINGTON   (United States)

^c YALE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34347211674     PISSN: 00754102     EISSN: 00754102     Source Type: Journal    
DOI: 10.1515/CRELLE.2006.097     Document Type: Article

References (27)

1. George M. Bergman, The logarithmic limit-set of an algebraic variety, Trans. Amer. Math. Soc. 157 (1971), 459-469.
2. Robert Bieri and J. R. J. Groves, The geometry of the set of characters induced by valuations, J. reine angew. Math. 347 (1984), 168-195.
3. Robert Bieri and Ralph Strebel, A geometric invariant for modules over an abelian group, J. reine angew. Math, 322 (1981), 170-189.
4. T. Bogart, A. Jensen, D. Speyer, B. Sturmfels, and R. Thomas, Computing tropical varieties, arXiv AG/0507563.
5. Fedor Bogomolov and Tihomir Petrov, Algebraic Curves and One-Dimensional Fields, American Mathematical Society, Providence 2002.
6. S. Bosch, V. Güntzer, and R. Remmert, Non-Archimedean Analysis, Springer, New York.
7. Nicolas Bourbaki, Commutative Algebra, Springer, Berlin 1989.
8. Mike Boyle and Douglas Lind, Expansive subdynamics, Trans. Amer. Math. Soc. 349 (1997), 55-102.
9. P. M. Cohn, Puiseux's theorem revisited, J. Pure Appl. Alg. 31 (1984), 1-4; correction, 52 (1988), 197-198.
10. B. Conrad, Irreducible components of rigid spaces, Ann. Inst. Fourier Grenoble 49 (1999), 473-541.
11. b-actions, Erg. Th. Dyn. Syst. 21 (2001), 1695-1729.
12. David Eisenbud, Commutative Algebra with a View toward Algebraic Geometry, Springer, New York 1995.
13. I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Birkhäuser, Boston 1994.
14. Fernando Q. Gouvêa, p-adic Numbers, 2nd Ed., Springer, New York 2000.
15. Kiran S. Kedlaya, The algebraic closure of the power series field in positive characteristic, Proc. Amer. Math. Soc. 129 (2001), 3461-3470.
16. d-actions, J. Amer. Math. Soc. 12 (1999), 953-980.
17. Douglas Lind, Klaus Schmidt, and Thomas Ward, Mahler measure and entropy for commuting automorphisms of compact groups, Invent. Math. 101 (1990), 593-629.
18. Grigory Mikhalkin, Amoebas of algebraic varieties, a report for the Real Algebraic and Analytic Geometry Congress, June 2001, Rennes, France, arXiv math.AG/0108225.
19. Grigory Mikhalkin, Amoebas of algebraic varieties and tropical geometry, arXiv math.AG/0403015.
20. Paulo Ribenboim, Fields: algebraically closed and others, Manuscr. Math. 75 (1992), 115-150.
21. Jürgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald, First steps in tropical geometry, Conference on Idempotent Mathematics and Mathematical Physics, Vienna 2003, G. L. Litvinov and V. P. Maslov, eds., arXiv math.AG/0306366.
22. Klaus Schmidt, Dynamical Systems of Algebraic Origin, Birkhäuser Verlag, Basel-Berlin-Boston 1995.
23. Erik Scott, Expansive Subdynamics of Algebraic Actions Generated by Principal Ideals in the Ring of Two-Variable Laurent Polynomials, Master's Thesis, University of Washington, 1999.
24. David Speyer and Bernd Sturmfels, The tropical Grassmannian, Adv. Geom. 4 (2004), 389-411.
25. Bernd Sturmfels, Gröbner Bases and Convex Polytopes, Amer. Math. Soc., Providence 1996.
26. Oleg Viro, Dequantization of real algebraic geometry on logarithmic paper, arXiv math.AG/0005163.
27. Oleg Viro, What is an amoeba?, Notices Amer. Math. Soc. 49 (2002), 916-917.