Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Intersection of a correspondence with a graph of Frobenius

Author: Yakov Varshavsky
Journal: J. Algebraic Geom. 27 (2018), 1-20
Published electronically: February 17, 2017
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Abstract | References | Additional Information

Abstract: The goal of this note is to give a short geometric proof of a theorem of Hrushovski asserting that an intersection of a correspondence with a graph of a sufficiently large power of Frobenius is non-empty.

References [Enhancements On Off] (What's this?)

  • [BS] Alexander Borisov and Mark Sapir, Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms, Invent. Math. 160 (2005), no. 2, 341-356. MR 2138070 (2006b:20033),
  • [De] Pierre Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273-307 (French). MR 0340258 (49 #5013)
  • [EM] Hélène Esnault and Vikram Mehta, Simply connected projective manifolds in characteristic $ p>0$ have no nontrivial stratified bundles, Invent. Math. 181 (2010), no. 3, 449-465. MR 2660450 (2012h:14048),
  • [Fa] Najmuddin Fakhruddin, Questions on self maps of algebraic varieties, J. Ramanujan Math. Soc. 18 (2003), no. 2, 109-122. MR 1995861 (2004f:14038)
  • [Fu] William Fulton, Intersection theory, 2nd ed., 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. 2, Springer-Verlag, Berlin, 1998. MR 1644323 (99d:14003)
  • [Gr] A. Grothendieck, rédigé par P. Deligne, La classe de cohomologie associées à un cycle, SGA $ 4\frac {1}{2}$, Lecture Notes in Math. 569, Springer-Verlag, New York, 1977, pp. 129-153.
  • [Hr] E. Hrushovski, The elementary theory of the Frobenius automorphism, preprint, available at˜ehud/FROB.pdf.
  • [dJ] A. J. de Jong, Smoothness, semi-stability and alterations, Inst. Hautes Études Sci. Publ. Math. 83 (1996), 51-93. MR 1423020 (98e:14011)
  • [KS] Kazuya Kato and Takeshi Saito, Ramification theory for varieties over a perfect field, Ann. of Math. (2) 168 (2008), no. 1, 33-96. MR 2415398 (2009h:14033),
  • [Laf] Laurent Lafforgue, Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math. 147 (2002), no. 1, 1-241 (French, with English and French summaries). MR 1875184 (2002m:11039),
  • [Lau] Gérard Laumon, Homologie étale, Séminaire de géométrie analytique (École Norm. Sup., Paris, 1974-75), Soc. Math. France, Paris, 1976, pp. 163-188. Astérisque, No. 36-37. MR 0444667 (56 #3017)
  • [Pi] Richard Pink, On the calculation of local terms in the Lefschetz-Verdier trace formula and its application to a conjecture of Deligne, Ann. of Math. (2) 135 (1992), no. 3, 483-525. MR 1166642 (93m:14017),
  • [Va] Yakov Varshavsky, Lefschetz-Verdier trace formula and a generalization of a theorem of Fujiwara, Geom. Funct. Anal. 17 (2007), no. 1, 271-319. MR 2306659 (2008d:14032),

Additional Information

Yakov Varshavsky
Affiliation: Institute of Mathematics, Hebrew University, Givat-Ram, Jerusalem, 91904, Israel

Received by editor(s): October 29, 2014
Received by editor(s) in revised form: November 28, 2014, and July 1, 2016
Published electronically: February 17, 2017
Additional Notes: This work was supported by The Israel Science Foundation (grant No. 1017/13)
Article copyright: © Copyright 2017 Universal Press, Inc.

American Mathematical Society