references.bib

@article {dejong,
    AUTHOR = {de Jong, A. J.},
     TITLE = {The moduli spaces of polarized abelian varieties},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
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}

@article {birkenhake-lange-2003,
    AUTHOR = {Birkenhake, Christina and Lange, Herbert},
     TITLE = {An isomorphism between moduli spaces of abelian varieties},
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  FJOURNAL = {Mathematische Nachrichten},
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}

@misc{rains,
Author = {Eric M. Rains},
Title = {Elliptic double affine {H}ecke algebras},
Year = {2017},
Eprint = {Available at arXiv:1709.02989},
}

@incollection {rosen-avc,
    AUTHOR = {Rosen, Michael},
     TITLE = {Abelian varieties over {${\bf C}$}},
 BOOKTITLE = {Arithmetic geometry ({S}torrs, {C}onn., 1984)},
     PAGES = {79--101},
 PUBLISHER = {Springer, New York},
      YEAR = {1986},
   MRCLASS = {14K20},
  MRNUMBER = {861973},
}

@incollection {milne-av,
    AUTHOR = {Milne, J. S.},
     TITLE = {Abelian varieties},
 BOOKTITLE = {Arithmetic geometry ({S}torrs, {C}onn., 1984)},
     PAGES = {103--150},
 PUBLISHER = {Springer, New York},
      YEAR = {1986},
   MRCLASS = {14K05 (11G10)},
  MRNUMBER = {861974},
}

@article {complex1996lenstra,
    AUTHOR = {Lenstra, Jr., H. W.},
     TITLE = {Complex multiplication structure of elliptic curves},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {56},
      YEAR = {1996},
    NUMBER = {2},
     PAGES = {227--241},
      ISSN = {0022-314X},
   MRCLASS = {11G20 (14G15 14H25)},
  MRNUMBER = {1373549},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1006/jnth.1996.0015},
       URL = {https://doi.org/10.1006/jnth.1996.0015},
}

@article {kani2011products,
    AUTHOR = {Kani, Ernst},
     TITLE = {Products of {CM} elliptic curves},
   JOURNAL = {Collect. Math.},
  FJOURNAL = {Collectanea Mathematica},
    VOLUME = {62},
      YEAR = {2011},
    NUMBER = {3},
     PAGES = {297--339},
      ISSN = {0010-0757},
   MRCLASS = {11G10 (11G15 14H52 14K02 14K22 14L15)},
  MRNUMBER = {2825715},
MRREVIEWER = {Joseph H. Silverman},
       DOI = {10.1007/s13348-010-0029-1},
       URL = {https://doi.org/10.1007/s13348-010-0029-1},
}

@article {ktheory1964bass,
    AUTHOR = {Bass, H.},
     TITLE = {{$K$}-theory and stable algebra},
   JOURNAL = {Inst. Hautes \'{E}tudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'{E}tudes Scientifiques. Publications
              Math\'{e}matiques},
    NUMBER = {22},
      YEAR = {1964},
     PAGES = {5--60},
      ISSN = {0073-8301},
   MRCLASS = {18.20 (16.90)},
  MRNUMBER = {0174604},
MRREVIEWER = {J. F. Adams},
       URL = {http://www.numdam.org/item?id=PMIHES_1964__22__5_0},
}

@phdthesis{kohel1996endomorphism,
  title={Endomorphism rings of elliptic curves over finite fields},
  author={Kohel, David},
  year={1996},
  school={University of California at Berkeley},
  url={http://echidna.maths.usyd.edu.au/~kohel/pub/thesis.pdf},
}

@book {cox2011primes,
  AUTHOR = {Cox, David A.},
  TITLE = {Primes of the form {$x^2 + ny^2$}},
  SERIES = {Pure and Applied Mathematics (Hoboken)},
  EDITION = {Second},
  PUBLISHER = {John Wiley \& Sons, Inc., Hoboken, NJ},
  YEAR = {2013},
  PAGES = {xviii+356},
  ISBN = {978-1-118-39018-4},
  MRCLASS = {11A41 (11F11 11R11 11R16 11R18 11R37 11Y11)},
  MRNUMBER = {3236783},
  MRREVIEWER = {Michael C. Berg},
  DOI = {10.1002/9781118400722},
  URL = {http://dx.doi.org/10.1002/9781118400722},
}


@book {krantz2017harmonic,
    AUTHOR = {Krantz, Steven G.},
     TITLE = {Harmonic and complex analysis in several variables},
    SERIES = {Springer Monographs in Mathematics},
 PUBLISHER = {Springer, Cham},
      YEAR = {2017},
     PAGES = {xii+424},
      ISBN = {978-3-319-63229-2; 978-3-319-63231-5},
   MRCLASS = {32-02 (32A50 32W05)},
  MRNUMBER = {3645453},
       DOI = {10.1007/978-3-319-63231-5},
       URL = {https://doi.org/10.1007/978-3-319-63231-5},
}

@book {bruinier2008the123,
    AUTHOR = {Bruinier, Jan Hendrik and van der Geer, Gerard and Harder,
              G\"{u}nter and Zagier, Don},
     TITLE = {The 1-2-3 of modular forms},
    SERIES = {Universitext},
      NOTE = {Lectures from the Summer School on Modular Forms and their
              Applications held in Nordfjordeid, June 2004,
              Edited by Kristian Ranestad},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2008},
     PAGES = {x+266},
      ISBN = {978-3-540-74117-6},
   MRCLASS = {11-06 (11F11)},
  MRNUMBER = {2385372},
       DOI = {10.1007/978-3-540-74119-0},
       URL = {https://doi.org/10.1007/978-3-540-74119-0},
}


@book {klingen1990introductory,
    AUTHOR = {Klingen, Helmut},
     TITLE = {Introductory lectures on {S}iegel modular forms},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {20},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1990},
     PAGES = {x+162},
      ISBN = {0-521-35052-2},
   MRCLASS = {11F46},
  MRNUMBER = {1046630},
MRREVIEWER = {Min Ho Lee},
       DOI = {10.1017/CBO9780511619878},
       URL = {https://doi.org/10.1017/CBO9780511619878},
}

@misc{multiparty,
    author = {Dan Boneh and Darren Glass and Daniel Krashen and Kristin Lauter and Shahed Sharif and Alice Silverberg and Mehdi Tibouchi and Mark Zhandry},
    title = {Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves},
    howpublished = {{T}o appear in {J}ournal of {M}athematical {C}ryptology},
    year = {},
    note = {Available at \url{https://eprint.iacr.org/2018/665}},
}

@article {katz1973padic,
    AUTHOR = {Katz, Nicholas M.},
     TITLE = {{$p$}-adic properties of modular schemes and modular forms},
 BOOKTITLE = {Modular functions of one variable, {III} ({P}roc. {I}nternat.
              {S}ummer {S}chool, {U}niv. {A}ntwerp, {A}ntwerp, 1972)},
     PAGES = {69--190. Lecture Notes in Mathematics, Vol. 350},
 PUBLISHER = {Springer, Berlin},
      YEAR = {1973},
   MRCLASS = {10D15 (14D20)},
  MRNUMBER = {0447119},
MRREVIEWER = {V. V. Sokurov},
}

@book {faltings1990degeneration,
    AUTHOR = {Faltings, Gerd and Chai, Ching-Li},
     TITLE = {Degeneration of abelian varieties},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results
              in Mathematics and Related Areas (3)]},
    VOLUME = {22},
      NOTE = {With an appendix by David Mumford},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1990},
     PAGES = {xii+316},
      ISBN = {3-540-52015-5},
   MRCLASS = {14K10 (11G10 14D20 14K25)},
  MRNUMBER = {1083353},
MRREVIEWER = {Min Ho Lee},
       DOI = {10.1007/978-3-662-02632-8},
       URL = {https://doi.org/10.1007/978-3-662-02632-8},
}

@book {git,
    AUTHOR = {Mumford, D. and Fogarty, J. and Kirwan, F.},
     TITLE = {Geometric invariant theory},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results
              in Mathematics and Related Areas (2)]},
    VOLUME = {34},
   EDITION = {Third},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1994},
     PAGES = {xiv+292},
      ISBN = {3-540-56963-4},
   MRCLASS = {14D25 (58E05 58F05)},
  MRNUMBER = {1304906},
MRREVIEWER = {Yi Hu},
       DOI = {10.1007/978-3-642-57916-5},
       URL = {https://doi.org/10.1007/978-3-642-57916-5},
}

@article {mumford1966,
    AUTHOR = {Mumford, D.},
     TITLE = {On the equations defining abelian varieties. {I}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {1},
      YEAR = {1966},
     PAGES = {287--354},
      ISSN = {0020-9910},
   MRCLASS = {14.51},
  MRNUMBER = {204427},
MRREVIEWER = {J. W. S. Cassels},
       DOI = {10.1007/BF01389737},
       URL = {https://doi.org/10.1007/BF01389737},
}