Xevi Guitart

Publications

• Evaluation of Bianchi Rigid Meromorphic Cocycles at Big ATR Points.
  L. Gehrmann, X. Guitart, M. Masdeu Preprint [abstract] [tables] [code]
• Punts racionals en corbes el·líptiques.
  X. Guitart, M. Masdeu. Butlletí de la Societat Catalana de Matemàtiques, 2025. [abstract]
• Periods of modular forms and applications to the conjectures of Oda and of Prasanna-Venkatesh.
  X. Guitart, S. Molina. Preprint [abstract]
• Abelian varieties genuinely of GL_n-type.
  F. Fité, E. Florit, X. Guitart. Preprint [abstract]
• Endomorphism algebras of geometrically 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. Poly. J. Math., Vol. 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).