Publications

  • Abelian varieties genuinely of GL_n-type.
    F. Fité, E. Florit, X. Guitart . Preprint [abstract]
  • Endomorphism algebras of geometricall split genus 2 Jacobians over Q.
    F. Fité, E. Florit, X. Guitart . Preprint [abstract]
  • Appendix to Polarized products of elliptic curves with complex multiplication and field of moduli Q.
    F. Narbonne, with an appendix by F. Fité and X. Guitart . Polynesian Journal of Mathematics, Volume 1, Issue 5, Pages 1-32. (Dec. 2024)
  • Plectic p-adic invariants
    M. Fornea, X. Guitart. M. Masdeu. . Adv. Math. 406 (2022), Paper No. 108484, 26 pp. [abstract]
  • Tate module tensor decompositions and Sato-Tate conjecture for varieties potentially of GL_2-type
    F. Fité, X. Guitart. Math. Z. 300 (2022), no. 3, 2975-2995 [abstract]
  • A quaternionic construction of $p$-adic singular moduli
    X. Guitart. M. Masdeu, X. Xarles. Res. Math. Sci. 8 (2021), no. 3, Paper No. 45, 20 pp. [abstract]
  • Special values of triple-product $p$-adic L-functions and non-crystalline diagonal classes
    F. Gatti, X. Guitart. M. Masdeu, V. Rotger. J. Theor. Nombres Bordeaux 33 (2021), no. 3, part 1, 809-834 [abstract]
  • On the elliptic Stark Conjecture in higher weight
    F. Gatti, X. Guitart. Publ. Mat. 64 (2020), 577-619 [abstract]
  • Endomorphism algebras of geometrically split abelian surfaces over Q
    F. Fité, X. Guitart. Algebra and Number Theory Vol. 14 (2020), No. 6, 1399-1421 [abstract]
  • An automorphic approach to Darmon points
    X. Guitart, M. Masdeu, S. Molina. Indiana Univ. Math. J. 69 (2020), no. 4, 1251-1274. [abstract]
  • Computing p-adic periods of abelian varieties from automorphic forms
    X. Guitart, M. Masdeu. Contemporary Mathematics, Volume 732, 2019. [abstract]
  • On the rank and the convergence rate towards the Sato-Tate measure
    F. Fité, X. Guitart. Int. Math. Res. Not., Vol. 2019 I. 13, July 2019, Pages 4081–4118 [abstract]
  • Periods of modular GL_2-type varieties and p-adic integration
    X. Guitart, M. Masdeu. Exp. Math. 27 (2018), no. 3, 344-361. [abstract]
  • Fields of definition of elliptic k-curves and the realizability of all genus 2 Sato-Tate groups over a number field
    F. Fité, X. Guitart. Trans. Amer. Math. Soc. Vol. 370, N. 7 (2018), 4623-4659 [abstract] [Erratum]
  • Uniformization of modular elliptic curves via p-adic periods
    X. Guitart, M. Masdeu, and H. Sengun. J. Algebra 445 (2016), 458-502. [abstract]
  • Darmon points on elliptic curves over number fields of arbitrary signature
    X. Guitart, M. Masdeu, and H. Sengun. P. Lond. Math. Soc. (3) 111 (2015), no. 2, 484-518. [abstract]
  • A p-adic construction of ATR points on Q-curves
    X. Guitart, M. Masdeu. Publ. Mat. 59 (2015), 511-545 [abstract]
  • Overconvergent cohomology and quaternionic Darmon points [abstract]
    X. Guitart, M. Masdeu. J. Lond. Math. Soc. (2) 90 (2014), no. 2, 495--524. [Sage code]
  • Elementary matrix decomposition and the computation of Darmon points with higher conductor
    X. Guitart, M. Masdeu. Math. Comp. 84 (2015), 875-893 [Sage code] [abstract]
  • Computation of ATR Darmon points on non-geometrically modular elliptic curves [abstract]
    X. Guitart, M. Masdeu. Exp. Math. 22(1): 85-98 (2013) [Sage code]
  • Almost totally complex points on elliptic curves [abstract]
    X. Guitart, V. Rotger, and Y. Zhao. Trans. Amer. Math. Soc. 336 (2014), 2773-2802[code]
  • Modular abelian varieties over number fields [abstract]
    X. Guitart, J. Quer. Canad. J. Math. 66 (2014), 170-196
  • Continued fractions in 2-stage euclidean quadratic fields [abstract]
    X. Guitart, M. Masdeu. Math. Comp. Vol. 82, N. 282, April 2013, pp. 1223–1233 [code]
  • Abelian varieties with many endomorphisms and their absolutely simple factors [abstract]
    X. Guitart. Rev. Mat. Iberoam. 28 (2012), no. 2, 591-601
  • Fields of definition of building blocks with quaternionic multiplication [abstract]
    X. Guitart. Acta Arith. 153 (2012), 1-14
  • Remarks on strongly modular Jacobian surfaces [abstract]
    X. Guitart, J. Quer. Journal de théorie des nombres de Bordeaux, 23 no. 1 (2011), p. 171-182
  • On the modularity level of modular abelian varieties over number fields [abstract]
    E. González-Jiménez, X, Guitart. J. Number Theory 130, no. 4, 1560-1570 (2010).
  • Parametrization of abelian K-surfaces with quaternionic multiplication [abstract]
    X. Guitart, S. Molina. C. R. Math. Acad. Sci. Paris 347 (2009), no. 23-24, 1325-1330.


    • Thesis

  • Arithmetic properties of abelian varieties under Galois conjugation (advisor: Jordi Quer).
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