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6 - A short course on geometric motivic integration

Published online by Cambridge University Press:  07 October 2011

Manuel Blickle
Affiliation:
Johannes Gutenberg-Universität Mainz
Raf Cluckers
Affiliation:
Université de Lille
Johannes Nicaise
Affiliation:
Katholieke Universiteit Leuven, Belgium
Julien Sebag
Affiliation:
Université de Rennes I, France
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References

[1] Dan, Abramovich, Kalle, Karu, Kenji, Matsuki, and Jarosław, Włodarczyk, Torification and factorization of birational maps, J. Amer. Math. Soc. 15 (2002), no. 3, 531–572 (electronic).Google Scholar
[2] Victor V., Batyrev, Stringy Hodge numbers of varieties with Goren-stein canonical singularities, Integrable systems and algebraic geometry (Kobe/Kyoto, 1997), World Sci. Publishing, River Edge, NJ, 1998, pp. 1–32.Google Scholar
[3] Victor V., Batyrev and Lev A., Borisov, Mirror duality and string-theoretic Hodge numbers, Invent. Math. 126 (1996), no. 1, 183–203.Google Scholar
[4] Franziska, Bittner, The universal Euler characteristic for varieties of characteristic zero, Compos. Math. 140 (2004), no. 4, 1011–1032.Google Scholar
[5] Siegfried, Bosch, Werner, Lütkebohmert, and Michel, Raynaud, Néron models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 21, Springer-Verlag, Berlin, 1990.Google Scholar
[6] Alastair, Craw, An introduction to motivic integration, Strings and geometry, Clay Math. Proc., vol. 3, Amer. Math. Soc., Providence, RI, 2004, pp. 203–225.Google Scholar
[7] Pierre, Deligne, Théorie de Hodge. I, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1, Gauthier-Villars, Paris, 1971, pp. 425–430.Google Scholar
[8] Pierre, Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. (1971), no. 40, 5–57.Google Scholar
[9] Pierre, Deligne, Théorie de Hodge. III, Inst. Hautes Études Sci. Publ. Math. (1974), no. 44, 5–77.Google Scholar
[10] Jan, Denef and François, Loeser, Geometry on arc spaces of algebraic varieties, In European Congress of Mathematics, Vol. I (Barcelona, 2000), 201:327–348. Progr. Math. Basel: Birkhäuser.
[11] Jan, Denef and François, Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999), 201–232, arXiv:math.AG/9803039.Google Scholar
[12] Jan, Denef and François, Loeser, Geometry on Arc Spaces, Notes of a talk available at http://www.wis.kuleuven.ac.be/algebra/NotesCambridge/.
[13] Lawrence, Ein, Robert, Lazarsfeld, and Mustaţăa, Mircea, Contact loci in arc spaces, Compos. Math. 140 (2004), no. 5, 1229–1244.Google Scholar
[14] Lawrence, Ein and Mustaţăa, Mircea, The log canonical threshold of homogeneous affine hypersurfaces, arXiv:math.AG/0105113.
[15] Lawrence, Ein and Mustaţăa, Mircea, Inversion of adjunction for local complete intersection varieties, Amer. J. Math. 126 (2004), no. 6, 1355–1365.Google Scholar
[16] Lawrence, Ein, Mustaţă, Mircea, and Yasuda, Takehiko, Jet schemes, log discrepancies and inversion of adjunction, Invent. Math. 153 (2003), no. 3, 519–535.Google Scholar
[17] David, Eisenbud, Commutative algebra, Springer-Verlag, New York, 1995.Google Scholar
[18] Marvin J., Greenberg, Schemata over local rings, Ann. of Math. (2) 73 (1961), 624–648.Google Scholar
[19] Marvin J., Greenberg, Schemata over local rings. II, Ann. of Math.(2) 78 (1963), 256–266.Google Scholar
[20] Marvin J., Greenberg, Rational points in Henselian discrete valuation rings, Inst. Hautes Études Sci. Publ. Math. (1966), no. 31, 59–64.Google Scholar
[21] Alexandre, Grothendieck, Éléments de géométrie algébrique. I. Le langage des schémas, Inst. Hautes Études Sci. Publ. Math. (1960), no. 4, 228.Google Scholar
[22] Alexandre, Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas IV, Inst. Hautes Études Sci. Publ. Math. (1967), no. 32, 361.Google Scholar
[23] Thomas C., Hales, Can p-adic integrals be computed?, Contributions to automorphic forms, geometry, and number theory, Johns Hopkins Univ. Press, Baltimore, MD, 2004, pp. 313–329.Google Scholar
[24] Thomas C., Hales, What is motivic measure?, Bull. Amer. Math. Soc. (N.S.) 42 (2005), no. 2, 119–135 (electronic).Google Scholar
[25] Robin, Hartshorne, Algebraic geometry, Springer, New York, 1973.Google Scholar
[26] Shihoko, Ishii and János, Kollár, The Nash problem on arc families of singularities, Duke Math. J. 120 (2003), no. 3, 601–620.Google Scholar
[27] Tetsushi, Ito, Stringy Hodge numbers and p-adic Hodge theory, Compos. Math. 140 (2004), no. 6, 1499–1517.Google Scholar
[28] János, Kollár, Singularities of pairs, Algebraic geometry—Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62, Amer. Math. Soc., Providence, RI, 1997, pp. 221–287.Google Scholar
[29] János, Kollár and Shigefumi, Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998, With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original.Google Scholar
[30] Maxim, Kontsevich, Lecture at Orsay, 1995.
[31] Robert, Lazarsfeld, Positivity in algebraic geometry. II, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 49, Springer-Verlag, Berlin, 2004, Positivity for vector bundles, and multiplier ideals.Google Scholar
[32] Eduard, Looijenga, Motivic measures, Astérisque (2002), no. 276, 267–297, Séminaire Bourbaki, Vol. 1999/2000.Google Scholar
[33] Mustaţăa, Mircea, Jet Schemes of Locally Complete Intersection Canonical Singularities, Invent. Math. 145 (2001), 397–424, arXiv:math.AG/0008002.CrossRefGoogle Scholar
[34] Mustaţăa, Mircea, Singularities of Pairs via Jet Schemes, J. Amer. Math. Soc. 15 (2002), 599–615, arXiv:math.AG/0102201.CrossRefGoogle Scholar
[35] John F., Nash Jr., Arc structure of singularities, DukeMath.J. 81 (1995), no. 1, 31–38 (1996), A celebration of John F. Nash, Jr.Google Scholar
[36] Niko, Naumann, Algebraic independence in the Grothendieck ring of varieties, Transactions of the American Mathematical Society 359, no. 4: 1653–1683 (electronic)
[37] Bjorn, Poonen, The Grothendieck ring of varieties is not a domain, Math. Res. Lett. 9 (2002), no. 4, 493–497.Google Scholar
[38] Miles, Reid, La correspondance de McKay, Astérisque (2002), no. 276, 53–72, Séminaire Bourbaki, Vol. 1999/2000.Google Scholar
[39] Julien, Sebag, Intégration motivique sur les schémas formels, Bull. Soc. Math. France 132 (2004), no. 1, 1–54.Google Scholar
[40] Vyacheslav V., Shokurov, Letters of a bi-rationalist. IV. Geometry of log flips, Algebraic geometry, de Gruyter, Berlin, 2002, pp. 313–328.Google Scholar
[41] Shunsuke, Takagi, F-singularities of pairs and Inversion of Adjunction of arbitrary codimension, Invent. Math. 157 (2004), no. 1, 123–146.Google Scholar
[42] Willem, Veys, Arc spaces, motivic integration and stringy invariants. In: S., Izumiya et al. (eds.), Singularity Theory and its applications, pages 529–572. Volume 43 of Advanced Studies in Pure Mathematics. Mathematical Society of Japan, Tokyo, 2006.Google Scholar
[43] Takehiko, Yasuda, Dimensions of jet schemes of log singularities, Amer. J. Math. 125 (2003), no. 5, 1137–1145.Google Scholar

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