@article {alz-pirola,
    AUTHOR = {Alzati, A. and Pirola, G. P.},
     TITLE = {Rational orbits on three-symmetric products of abelian
              varieties},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {337},
      YEAR = {1993},
    NUMBER = {2},
     PAGES = {965--980},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {14K05 (14C15 14H40)},
  MRNUMBER = {93h:14035},
MRREVIEWER = {Claudio Pedrini},
}


@article {anderson,
    AUTHOR = {Anderson, Greg W. and Indik, Robert},
     TITLE = {On primes of degree one in function fields},
   JOURNAL = {Proc. Amer. Math. Soc.},
  FJOURNAL = {Proceedings of the American Mathematical Society},
    VOLUME = {94},
      YEAR = {1985},
    NUMBER = {1},
     PAGES = {31--32},
      ISSN = {0002-9939},
     CODEN = {PAMYAR},
   MRCLASS = {11R58 (14H25)},
  MRNUMBER = {86h:11107},
MRREVIEWER = {K. Kiyek},
}






@article {artin,
    AUTHOR = {Artin, M.},
     TITLE = {Supersingular {$K3$} surfaces},
   JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
    VOLUME = {7},
      YEAR = {1974},
     PAGES = {543--567 (1975)},
   MRCLASS = {14J25 (14G15)},
  MRNUMBER = {51 \#8116},
MRREVIEWER = {J. S. Milne},
}



@article {beauville,
    AUTHOR = {Beauville, Arnaud},
     TITLE = {Counting rational curves on {$K3$} surfaces},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {97},
      YEAR = {1999},
    NUMBER = {1},
     PAGES = {99--108},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {14N10 (11F23 14H40 14J28)},
MRREVIEWER = {Jim A. Bryan},
}

@article {bt,
    AUTHOR = {Bogomolov, Fedor and Tschinkel, Yuri},
     TITLE = {Density of rational points on elliptic {$K3$} surfaces},
   JOURNAL = {Asian J. Math.},
  FJOURNAL = {The Asian Journal of Mathematics},
    VOLUME = {4},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {351--368},
      ISSN = {1093-6106},
   MRCLASS = {14G05 (11G05 11G35 14C22 14J10 14J28)},
MRREVIEWER = {Matthew H. Baker},
}


 
 

 


@article {bryan,
    AUTHOR = {Bryan, Jim and Leung, Naichung Conan},
     TITLE = {The enumerative geometry of {$K3$} surfaces and modular forms},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {13},
      YEAR = {2000},
    NUMBER = {2},
     PAGES = {371--410},
      ISSN = {0894-0347},
   MRCLASS = {14N10 (11F23 14J28 14N35)},
MRREVIEWER = {Gary P. Kennedy},
}

@misc{candelas,
AUTHOR = {Candelas, Philip and de la Ossa, Xenia  and Rodriguez-Villegas, Fernando},
TITLE =  {Calabi-{Y}au manifolds over finite fields, {I}},
YEAS  =  {2000},
NOTE  =  {{\tt hep-th/0012233}},
} 


@article {chen,
    AUTHOR = {Chen, Xi},
     TITLE = {A simple proof that rational curves on {$K3$} are nodal},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {324},
      YEAR = {2002},
    NUMBER = {1},
     PAGES = {71--104},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {14J28 (14H20)},
MRREVIEWER = {Lucia Caporaso},
}

@book {dolgachev,
    AUTHOR = {Cossec, Fran{\c{c}}ois R. and Dolgachev, Igor V.},
     TITLE = {Enriques surfaces. {I}},
    SERIES = {Progress in Mathematics},
    VOLUME = {76},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {1989},
     PAGES = {x+397},
      ISBN = {0-8176-3417-7},
   MRCLASS = {14J28},
  MRNUMBER = {90h:14052},
MRREVIEWER = {Ulf Persson},
}


@article {deligne,
    AUTHOR = {Deligne, Pierre},
     TITLE = {La conjecture de {W}eil pour les surfaces {$K3$}},
   JOURNAL = {Invent. Math.},
    VOLUME = {15},
      YEAR = {1972},
     PAGES = {206--226},
   MRCLASS = {14G13},
MRREVIEWER = {M. Fried},
}



 
 

 

@article {edix,
    AUTHOR = {Edixhoven, S. J. and Moonen, B. J. J. and Oort, F.},
     TITLE = {Open problems in algebraic geometry},
   JOURNAL = {Bull. Sci. Math.},
  FJOURNAL = {Bulletin des Sciences Math\'ematiques},
    VOLUME = {125},
      YEAR = {2001},
    NUMBER = {1},
     PAGES = {1--22},
      ISSN = {0007-4497},
     CODEN = {BSMQA9},
   MRCLASS = {14-02 (11-02 11F41 11G10 11G18)},
  MRNUMBER = {2002a:14001},
MRREVIEWER = {Carlo Gasbarri},
}


 
 

@incollection {ellenberg,
    AUTHOR = {Ellenberg, Jordan S.},
     TITLE = {{$K3$} surfaces over number fields with geometric {P}icard
              number one},
 BOOKTITLE = {Arithmetic of higher-dimensional algebraic varieties (Palo
              Alto, CA, 2002)},
    SERIES = {Progr. Math.},
    VOLUME = {226},
     PAGES = {135--140},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {2004},
   MRCLASS = {11G35 (14G25 14J28)},
  MRNUMBER = {2 029 866},
}


 
 


@book {fried-jarden,
    AUTHOR = {Fried, Michael D. and Jarden, Moshe},
     TITLE = {Field arithmetic},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3)},
    VOLUME = {11},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1986},
     PAGES = {xviii+458},
      ISBN = {3-540-16640-8},
   MRCLASS = {12Lxx (03B25 03C10 03C60 03H05)},
  MRNUMBER = {89b:12010},
MRREVIEWER = {R. Weissauer},
}




@article {harris-t,
    AUTHOR = {Harris, Joe and Tschinkel, Yuri},
     TITLE = {Rational points on quartics},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {104},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {477--500},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {14G05 (11G35 14G25 14J20)},
}

@article {katsura,
    AUTHOR = {Katsura, Toshiyuki},
     TITLE = {Generalized {K}ummer surfaces and their unirationality in
              characteristic {$p$}},
   JOURNAL = {J. Fac. Sci. Univ. Tokyo Sect. IA Math.},
  FJOURNAL = {Journal of the Faculty of Science. University of Tokyo.
              Section IA. Mathematics},
    VOLUME = {34},
      YEAR = {1987},
    NUMBER = {1},
     PAGES = {1--41},
      ISSN = {0040-8980},
     CODEN = {JFTMAT},
   MRCLASS = {14J28 (14J25)},
  MRNUMBER = {88c:14055},
MRREVIEWER = {Piotr Blass},
}

@article {katz,
    AUTHOR = {Katz, Nicholas M.},
     TITLE = {Space filling curves over finite fields},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {6},
      YEAR = {1999},
    NUMBER = {5-6},
     PAGES = {613--624},
      ISSN = {1073-2780},
   MRCLASS = {11G20 (11G10 11G25 14G15)},
  MRNUMBER = {2001e:11067},
MRREVIEWER = {Arnaldo L. P. Garc{\'{\i}}a},
}
@book {katz1,
    AUTHOR = {Katz, Nicholas M.},
     TITLE = {Twisted {$L$}-functions and monodromy},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {150},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, NJ},
      YEAR = {2002},
     PAGES = {viii+249},
      ISBN = {0-691-09150-1; 0-691-09151-X},
   MRCLASS = {11G40 (11G05 11G25 14G05 14G10)},
  MRNUMBER = {2003i:11087},
MRREVIEWER = {Philippe G. Michel},
}




 
 

 


@article {mckinnon,
    AUTHOR = {McKinnon, David},
     TITLE = {Counting rational points on {$K3$} surfaces},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {84},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {49--62},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {14G05 (11G35 14J28)},
}

@incollection {mori-mukai,
    AUTHOR = {Mori, Shigefumi and Mukai, Shigeru},
     TITLE = {The uniruledness of the moduli space of curves of genus
              {$11$}},
 BOOKTITLE = {Algebraic geometry (Tokyo/Kyoto, 1982)},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {1016},
     PAGES = {334--353},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1983},
   MRCLASS = {14H10 (14D20 14J28)},
  MRNUMBER = {85b:14033},
MRREVIEWER = {Allen Tannenbaum},
}





@book {mumford,
    AUTHOR = {Mumford, David},
     TITLE = {Abelian varieties},
    SERIES = {Tata Institute of Fundamental Research Studies in Mathematics,
              No. 5 },
 PUBLISHER = {Published for the Tata Institute of Fundamental Research,
              Bombay},
      YEAR = {1970},
     PAGES = {viii+242},
   MRCLASS = {14.51},
  MRNUMBER = {44 \#219},
MRREVIEWER = {J. S. Milne},
}






@article {pirola,
    AUTHOR = {Pirola, Gian Pietro},
     TITLE = {Curves on generic {K}ummer varieties},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {59},
      YEAR = {1989},
    NUMBER = {3},
     PAGES = {701--708},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {14H40 (14H10 14K99)},
  MRNUMBER = {91b:14029},
MRREVIEWER = {Gang Xiao},
}


@incollection {pop,
    AUTHOR = {Pop, Florian and Saidi, Mohamed},
     TITLE = {On the specialization homomorphism of fundamental groups
of curves in positive characteristic},
 EDITOR    = {Schneps, Leila},
 BOOKTITLE = {Galois groups and fundamental groups},
    SERIES = {MSRI Publications},
    VOLUME = {41},
     PAGES = {107--118},
 PUBLISHER = {Cambridge Univ. Press},
      YEAR = {2003},
}


@article {oort-dejong,
    AUTHOR = {Oort, F. and de Jong, J.},
     TITLE = {Hyperelliptic curves in abelian varieties},
      NOTE = {Algebraic geometry, 5},
   JOURNAL = {J. Math. Sci.},
  FJOURNAL = {Journal of Mathematical Sciences},
    VOLUME = {82},
      YEAR = {1996},
    NUMBER = {1},
     PAGES = {3211--3219},
      ISSN = {1072-3374},
     CODEN = {JMTSEW},
   MRCLASS = {14K10 (14F20 14H45)},
  MRNUMBER = {97j:14052},
MRREVIEWER = {Takashi Ichikawa},
}

@incollection {oguiso,
    AUTHOR = {Oguiso, Keiji},
     TITLE = {On the complete classification of {C}alabi-{Y}au threefolds of
              type {${\rm III}\sb 0$}},
 BOOKTITLE = {Higher-dimensional complex varieties (Trento, 1994)},
     PAGES = {329--339},
 PUBLISHER = {de Gruyter},
   ADDRESS = {Berlin},
      YEAR = {1996},
   MRCLASS = {14J32 (14J30)},
  MRNUMBER = {98h:14047},
MRREVIEWER = {Mark Gross},
}


 
 

 

@article {poonen,
    AUTHOR = {Poonen, Bjorn},
     TITLE = {N\'eron-{T}ate projection of algebraic points},
   JOURNAL = {Internat. Math. Res. Notices},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2001},
    NUMBER = {9},
     PAGES = {435--440},
      ISSN = {1073-7928},
   MRCLASS = {14K15 (11G50 14G40)},
  MRNUMBER = {2002g:14065},
MRREVIEWER = {Antoine Chambert-Loir},
}


@incollection {shaf-rudakov1,
    AUTHOR = {Rudakov, A. N. and Shafarevich, I. R.},
     TITLE = {Surfaces of type {$K3$} over fields of finite characteristic},
 BOOKTITLE = {Current problems in mathematics, Vol. 18},
     PAGES = {115--207},
 PUBLISHER = {Akad. Nauk SSSR},
      YEAR = {1981},
   MRCLASS = {14J25 (14D15 14J10)},
  MRNUMBER = {83c:14027},
MRREVIEWER = {P. E. Newstead},
}

@article {shaf-rudakov,
    AUTHOR = {Rudakov, A. N. and Shafarevich, I. R.},
     TITLE = {Supersingular {$K3$} surfaces over fields of characteristic
              {$2$}},
   JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
  FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
    VOLUME = {42},
      YEAR = {1978},
    NUMBER = {4},
     PAGES = {848--869},
      ISSN = {0373-2436},
   MRCLASS = {14J25 (14J10)},
  MRNUMBER = {80e:14015},
MRREVIEWER = {Miles Reid},
}

@book {serre,
    AUTHOR = {Serre, Jean-Pierre},
     TITLE = {Lectures on the {M}ordell-{W}eil theorem},
    SERIES = {Aspects of Mathematics},
   EDITION = {Third},
 PUBLISHER = {Friedr. Vieweg \& Sohn},
   ADDRESS = {Braunschweig},
      YEAR = {1997},
     PAGES = {x+218},
}
@incollection {kollar,
    AUTHOR = {Araujo, Carolina and Koll{\'a}r, J{\'a}nos},
     TITLE = {Rational curves on varieties},
 BOOKTITLE = {Higher dimensional varieties and rational points (Budapest,
              2001)},
    SERIES = {Bolyai Soc. Math. Stud.},
    VOLUME = {12},
     PAGES = {13--68},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2003},
}








@article {shioda,
    AUTHOR = {Shioda, Tetsuji},
     TITLE = {Some results on unirationality of algebraic surfaces},
   JOURNAL = {Math. Ann.},
    VOLUME = {230},
      YEAR = {1977},
    NUMBER = {2},
     PAGES = {153--168},
   MRCLASS = {14J25 (14G20)},
  MRNUMBER = {58 \#28004},
}


@article {voisin,
    AUTHOR = {Voisin, Claire},
     TITLE = {Miroirs et involutions sur les surfaces {$K3$}},
      NOTE = {Journ\'ees de G\'eom\'etrie Alg\'ebrique d'Orsay (Orsay,
              1992)},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {218},
      YEAR = {1993},
     PAGES = {273--323},
      ISSN = {0303-1179},
   MRCLASS = {14J32 (14J15 14J28 32J17 32J27)},
  MRNUMBER = {95j:14051},
MRREVIEWER = {I. Dolgachev},
}






 
 @article {wan,
    AUTHOR = {Wan, Da Qing},
     TITLE = {Hilbert sets and zeta functions over finite fields},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {427},
      YEAR = {1992},
     PAGES = {193--207},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G25 (12E25 14G15)},
  MRNUMBER = {93c:11044},
MRREVIEWER = {S. D. Cohen},
}


@article {weil,
    AUTHOR = {Weil, Andr{\'e}},
     TITLE = {Zum {B}eweis des {T}orellischen {S}atzes},
   JOURNAL = {Nachr. Akad. Wiss. G\"ottingen. Math.-Phys. Kl. IIa.},
    VOLUME = {1957},
      YEAR = {1957},
     PAGES = {33--53},
   MRCLASS = {14.0X},
  MRNUMBER = {19,683e},
MRREVIEWER = {T. Matsusaka},
}


 
 
 

 @article {yau,
    AUTHOR = {Yau, Shing-Tung and Zaslow, Eric},
     TITLE = {B{PS} states, string duality, and nodal curves on {$K3$}},
   JOURNAL = {Nuclear Phys. B},
  FJOURNAL = {Nuclear Physics. B},
    VOLUME = {471},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {503--512},
      ISSN = {0550-3213},
     CODEN = {NUPBBO},
   MRCLASS = {14N10 (14J28 81T30)},
}