Equivariant motivic integration on formal schemes and the motivic zeta function

References

• Bittner, F. (2005). On motivic zeta functions and the motivic nearby fiber. Math. Z. 249(1):63–83. DOI: 10.1007/s00209-004-0689-1.
   Web of Science ®Google Scholar
• Bosch, S., Lütkebohmert, W. (1993). Formal and rigid geometry. I. Math. Ann. 295(1):291–317. DOI: 10.1007/BF01444889.
   Google Scholar
• Bosch, S., Lütkebohmert, W., Raynaud, M. (1990). Néron Models, Volume 21 of Ergebnisse der mathematik und ihrer grenzgebiete (3) [Results in Mathematics and Related Areas (3)]. Berlin: Springer-Verlag.
   Google Scholar
• Bosch, S., Lütkebohmert, W., Raynaud, M. (1995). Formal and rigid geometry. Math. Ann. 302(1):1–29. DOI: 10.1007/BF01444485.
   Web of Science ®Google Scholar
• Bosch, S., Schlöter, K. (1995). Néron models in the setting of formal and rigid geometry. Math. Ann. 301(1):339–362. DOI: 10.1007/BF01446633.
   Google Scholar
• Chambert-Loir, A., Nicaise, J., Sebag, J. (2016). Motivic Integration. To appear. In: Progress in Mathematics, Birkhaüser (571 pages).
   Google Scholar
• Conrad, B. (1999). Irreducible components of rigid spaces. Ann. Inst. Fourier (Grenoble) 49(2):473–541. Available at: http://www.numdam.org/item?id=AIF_1999__49_2_473_0.
   Web of Science ®Google Scholar
• Denef, J., Loeser, F. (1998). Motivic Igusa zeta functions. J. Algebraic Geom. 7(3):505–537.
   Web of Science ®Google Scholar
• Denef, J., Loeser, F. (2001). Geometry on Arc Spaces of Algebraic Varieties. In: Casacuberta, C., Miró-Roig, R. M., Verdera, J., Xambó-Descamps, S., eds. European Congress of Mathematics, Vol. 201. (Barcelona, 2000), Volume 201 of Progress in Mathematics. Birkhäuser, Basel: Progress in Mathematics.
   Google Scholar
• Eisenbud, D. (1995). Commutative Algebra, Volume 150 of Graduate Texts in Mathematics. New York: Springer-Verlag. With a view toward algebraic geometry. DOI: 10.1007/978-1-4612-5350-1.
   Google Scholar
• Esnault, H., Nicaise, J. (2011). Finite group actions, rational fixed points and weak Néron models. Pure Appl. Math. Q. 7(4):1209–1240.
   Web of Science ®Google Scholar
• Greenberg, M. J. (1961). Schemata over local rings. Ann. Math. (2) 73(3):624–648.
   Web of Science ®Google Scholar
• Grothendieck, A. (1961). Éléments de géométrie algébrique. II. Étude globale élémentaire de quelques classes de morphismes. Publications Mathématiques De L’institut. Des. Hautes. Scientifiques 8(1):5.
   Google Scholar
• Grothendieck, A. (1963). Revêtements étales et groupe fondamental. Fasc. I: Exposés 1 à 5, volume 1960/61 of Séminaire de Géométrie Algébrique. Paris: Institut des Hautes Études Scientifiques.
   Google Scholar
• Grothendieck, A. (1966). Éléments de géométrie algébrique. IV. Étude Locale Des Schémas Et Des Morphismes De Schémas. III. Inst. Hautes Études Sci. Publ. Math. 28:255.
   Google Scholar
• Hartmann, A. (2015). On rational points of varieties over local fields having a model with tame quotient singularities. Trans. Amer. Math. Soc. 367(11):8199–8227. DOI: 10.1090/S0002-9947-2015-06291-6.
   Web of Science ®Google Scholar
• Hartmann, A. (2016). The quotient map on the equivariant Grothendieck ring of varieties. Manuscripta Math. Math. 151(3–4):419–451. DOI: 10.1007/s00229-016-0842-2.
   Web of Science ®Google Scholar
• Halle, L. H., Nicaise, J. (2011). Motivic zeta functions of abelian varieties, and the monodromy conjecture. Adv. Math. 227(1):610–653. DOI: 10.1016/j.aim.2011.02.011.
   Web of Science ®Google Scholar
• Liu, Q. (2002). Algebraic geometry and arithmetic curves. Oxford Graduate Texts in Mathematics. Vol. 6. Oxford: Oxford University Press. Translated from the French by Reinie Erné, Oxford Science Publications.
   Google Scholar
• Loeser, F., Sebag, J. (2003). Motivic integration on smooth rigid varieties and invariants of degenerations. Duke Math. J. 119(2):315–344. DOI: 10.1215/S0012-7094-03-11924-9.
   Web of Science ®Google Scholar
• Nicaise, J. (2009). A trace formula for rigid varieties, and motivic Weil generating series for formal schemes. Math. Ann. 343(2):285–349. doi:10.1007/s00208-008-0273-9.
   Web of Science ®Google Scholar
• Nicaise, J. (2010). An introduction to p-adic and motivic zeta functions and the monodromy conjecture. In: Gautami, B., Kohji, M., Hirofumi, T., eds. Algebraic and Analytic Aspects of Zeta Functions and L-Functions, Volume 21 of MSJ Memoirs. Tokyo: Mathematical Society of Japan, pp. 141–166.
   Google Scholar
• Nicaise, J., Sebag, J. (2007). Motivic Serre invariants of curves. Manuscripta Math. 123(2):105–132-. DOI: 10.1007/s00229007-0088-0.
   Web of Science ®Google Scholar
• Nicaise, J., Sebag, J. (2007). Motivic Serre invariants, ramification, and the analytic Milnor fiber. Invent. Math. Math. 168(1):133–173. DOI: 10.1007/s00222-006-0029-7.
   Web of Science ®Google Scholar
• Nicaise, J., Sebag, J. (2008). Motivic Serre invariants and Weil restriction. J. Algebra 319(4):1585–1610. DOI: 10.1016/j.jalgebra.2007.11.006.
   Web of Science ®Google Scholar
• Nicaise, J., Sebag, J. (2011). Motivic invariants of rigid varieties, and applications to complex singularities. In: Cluckers, R., Nicaise, J., Sebag, J., eds. Motivic Integration and Its Interactions with Model Theory and Non-Archimedean Geometry. Volume I, Volume 383 of London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, pp. 244–304.
   Google Scholar
• Nicaise, J., Sebag, J. (2011). The Grothendieck ring of varieties. In: Cluckers, R., Nicaise, J., Sebag, J., eds. Motivic Integration and Its Interactions with Model Theory and Non-Archimedean Geometry. Volume I, Volume 383 of London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press, pp. 145–188.
   Google Scholar
• Sebag, J. (2004). Intégration motivique sur les schémas formels. Bull. Soc. Math. France 132(1):1–54.
   Google Scholar