% =============================================================================
% BibTeX Bibliography for:
% "Algebraic Cycles on Discrete K\"ahler Manifolds:
%  A Simplicial Proof of the Hodge Conjecture"
% Author: Rafael D. De Paz
% =============================================================================

% --- The Hodge Conjecture ---

@article{Hodge1941,
  author    = {Hodge, W. V. D.},
  title     = {The Theory and Applications of Harmonic Integrals},
  publisher = {Cambridge University Press},
  year      = {1941}
}

@misc{ClayHodge,
  author    = {{Clay Mathematics Institute}},
  title     = {The {H}odge {C}onjecture},
  year      = {2000},
  url       = {https://www.claymath.org/millennium/hodge-conjecture/},
  note      = {Millennium Prize Problem, official problem statement by P.~Deligne}
}

@article{Deligne2000,
  author    = {Deligne, Pierre},
  title     = {The {H}odge {C}onjecture},
  journal   = {Clay Mathematics Institute Millennium Prize Problems},
  year      = {2000},
  url       = {https://www.claymath.org/millennium/hodge-conjecture/}
}

% --- Algebraic Geometry and Cycles ---

@book{Voisin2002,
  author    = {Voisin, Claire},
  title     = {Hodge Theory and Complex Algebraic Geometry, {I} and {II}},
  series    = {Cambridge Studies in Advanced Mathematics},
  volume    = {76, 77},
  publisher = {Cambridge University Press},
  year      = {2002}
}

@book{GriffithsHarris1978,
  author    = {Griffiths, Phillip and Harris, Joseph},
  title     = {Principles of Algebraic Geometry},
  publisher = {Wiley-Interscience},
  year      = {1978}
}

@article{Totaro1997,
  author    = {Totaro, Burt},
  title     = {Torsion algebraic cycles and complex cobordism},
  journal   = {Journal of the American Mathematical Society},
  volume    = {10},
  number    = {2},
  pages     = {467--493},
  year      = {1997}
}

% --- Discrete Harmonic Forms and Simplicial Complexes ---

@article{Eckmann1945,
  author    = {Eckmann, Beno},
  title     = {Harmonische {F}unktionen und {R}andwertaufgaben in einem {K}omplex},
  journal   = {Commentarii Mathematici Helvetici},
  volume    = {17},
  pages     = {240--255},
  year      = {1945}
}

@article{Dodziuk1976,
  author    = {Dodziuk, Jozef},
  title     = {Finite-difference approach to the {H}odge theory of harmonic forms},
  journal   = {American Journal of Mathematics},
  volume    = {98},
  number    = {1},
  pages     = {79--104},
  year      = {1976}
}

@article{Friedman1998,
  author    = {Friedman, Joel},
  title     = {Computing {B}etti numbers via combinatorial {L}aplacians},
  journal   = {Algorithmica},
  volume    = {21},
  pages     = {331--346},
  year      = {1998}
}

@article{Desbrun2005,
  author    = {Desbrun, Mathieu and Hirani, Anil N. and Leok, Melvin and Marsden, Jerrold E.},
  title     = {Discrete Exterior Calculus},
  journal   = {arXiv:math/0508341},
  year      = {2005}
}

% --- Quantum Gravity and Discreteness ---

@article{Rovelli2004,
  author    = {Rovelli, Carlo},
  title     = {Quantum Gravity},
  publisher = {Cambridge University Press},
  year      = {2004},
  journal   = {Cambridge Monographs on Mathematical Physics}
}

@article{Loll1998,
  author    = {Loll, Renate},
  title     = {Discrete approaches to quantum gravity in four dimensions},
  journal   = {Living Reviews in Relativity},
  volume    = {1},
  number    = {13},
  year      = {1998}
}

@article{Baez1998,
  author    = {Baez, John C.},
  title     = {Spin foam models},
  journal   = {Classical and Quantum Gravity},
  volume    = {15},
  number    = {7},
  pages     = {1827--1858},
  year      = {1998}
}


@article{deligne1974conjecture,
  title={La conjecture de Weil: I},
  author={Deligne, Pierre},
  journal={Publications Math{'e}matiques de l'IH{'E}S},
  volume={43},
  pages={273--307},
  year={1974},
  publisher={Springer}
}
@book{griffiths1978principles,
  title={Principles of algebraic geometry},
  author={Griffiths, Phillip and Harris, Joseph},
  year={1978},
  publisher={John Wiley \& Sons}
}