Gerard Freixas i Montplet

Research

My research focuses on algebraic and arithmetic geometry, especially intersection theory, Arakelov theory, and moduli spaces. Below is the list of publications and attached files, which may differ slightly from the published versions:

Preprints

• D. Eriksson and G. Freixas i Montplet, The Deligne-Riemann-Roch isomorphism , arXiv:2509.05077 [math.AG], 91 pp.

Peer-Reviewed Journal Articles

• D. Eriksson, G. Freixas i Montplet and R. Wentworth, Complex Chern-Simons bundles in the relative setting , Astérisque (to appear), 144 pp.
• D. Eriksson and G. Freixas i Montplet, The spectral genus of an isolated hypersurface singularity and its relation to the Milnor number and analytic torsion , Documenta. Math. (to appear), 33 pp.
• D. Eriksson and G. Freixas i Montplet, Deligne-Riemann-Roch and intersection bundles , J. Éc. polytech. Math. 11 (2024), 247–361.
• D. Eriksson, G. Freixas i Montplet and C. Mourougane, On genus one mirror symmetry in higher dimensions and the BCOV conjectures , Forum of Mathematics, Pi 10 (2022), e19, 1–53.
• G. Freixas i Montplet, Du local au global en géométrie d'Arakelov , Gazette des Mathématiciens 169 (2021), SMF.
• D. Eriksson, G. Freixas i Montplet and C. Mourougane, BCOV invariants of Calabi-Yau manifolds and degenerations of Hodge structures , Duke Math. J. 170 (2021), no. 3, 379–454.
• G. Freixas i Montplet and A. von Pippich, Riemann-Roch isometries in the non-compact orbifold setting , J. Eur. Math. Soc. 22 (2020), no. 11, 3491–3564.
• G. Freixas i Montplet and R. Wentworth, Deligne pairings and families of rank one local systems on algebraic curves , J. Differential Geom. 115 (2020), no. 3, 475–528.
• G. Freixas i Montplet and R. Wentworth, Flat line bundles and the Cappell-Miller torsion in Arakelov geometry , Ann. Sci. Éc. Norm. Supér. (4) 52 (2019), no. 5, 1265–1303.
• D. Eriksson, G. Freixas i Montplet and C. Mourougane, Singularities of metrics on Hodge bundles and their topological invariants , Algebr. Geom. 5 (6) (2018), 742–775.
• G. Freixas i Montplet and S. Sankaran, Twisted Hilbert modular surfaces, arithmetic intersections and the Jacquet-Langlands correspondence , Adv. Math. 329 (2018), 1–84.
• R. Berman and G. Freixas i Montplet, An arithmetic Hilbert-Samuel theorem for singular metrics and cusp forms , Compos. Math. 150 (2014), 1703–1728.
• J. I. Burgos Gil, G. Freixas i Montplet and R. Litcanu, The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms , Ann. Fac. Sci. Toulouse 23 (2014), 513–559.
• J. I. Burgos Gil, G. Freixas i Montplet and R. Litcanu, Generalized holomorphic analytic torsion , J. Eur. Math. Soc. 16 (2014), 463–535.
• J.-B. Bost and G. Freixas i Montplet, Semi-abelian schemes and heights of cycles in moduli spaces of abelian varieties , Rend. Semin. Mat. Univ. Padova 128 (2012), 55–89.
• J. I. Burgos Gil, G. Freixas i Montplet and R. Litcanu, Hermitian structures on the derived category of coherent sheaves , J. Math. Pures Appl. 97 (2012), 424–499.
• G. Freixas i Montplet, An arithmetic Hilbert-Samuel theorem for pointed stable curves , J. Eur. Math. Soc. 14 (2012), 321–351.
• G. Freixas i Montplet, The Jacquet-Langlands correspondence and the arithmetic Riemann-Roch theorem for pointed curves , Int. J. Number Theory 8 (2012), 1–29.
• G. Freixas i Montplet, An Arakelov tautological boundary divisor on M_{1,1} , Collect. Math. 63 (2012), 243–259.
• G. Freixas i Montplet, An arithmetic Riemann-Roch theorem for pointed stable curves , Ann. Sci. Éc. Norm. Supér. (4) 42 (2009), 335–369.
• G. Freixas i Montplet, Heights and metrics with logarithmic singularities , J. Reine Angew. Math. 627 (2009), 97–153.

Refereed Conference Proceedings

• G. Freixas i Montplet, The arithmetic Riemann-Roch theorem and the Jacquet-Langlands correspondence , in "Arakelov Geometry and Diophantine Applications", Lect. Notes Math. 2276 (2021), 403–432, Springer.
• G. Freixas i Montplet, The Riemann-Roch theorem in Arakelov geometry , in "Algebraic Geometry and Number Theory", Progress in Mathematics 321 (2017), 91–133, Birkhäuser.
• J. I. Burgos Gil, G. Freixas i Montplet and R. Litcanu, Some recent results on generalized analytic torsion classes , AIP Conf. Proc. 1329, 49–69 (2011), Amer. Inst. Phys.

Book Chapters

• G. Freixas i Montplet, An introduction to Hodge-Tate decompositions , in "An excursion into p-adic Hodge theory", Panoramas et Synthèses (SMF) 54 (2019), 1–17.

Editorial Work

• P. Charollois, G. Freixas i Montplet and V. Maillot (eds.), Arithmetic L-functions and Differential Geometric Methods. Regulators IV , Progress in Math. 338 (2021), 324 pp., Birkhäuser.