Research articles
- D. Barrera, A. Cauchi, S. Molina, V. Rotger, Kato's theorem for elliptic curves over totally real number fields, in progress.
- H. Darmon, A. Lauder, V. Rotger, Elliptic Stark conjectures and exceptional weight one forms, submitted.
- O. Rivero, V. Rotger, Eisenstein congruences among Euler systems, to appear in Canadian Math. Bull.
- O. Rivero, V. Rotger, Motivic congruences and Sharifi's conjecture, to appear in American J. Math.
- F. Gatti, V. Rotger, Kolyvagin classes versus non-cristalline diagonal classes, submitted.
- H. Darmon, M. Harris, V. Rotger, A. Venkatesh, Derived Hecke algebra for dihedral weight one forms, Michigan Math. J. 72, 145-207 (2022). Special volume dedicated to Gopal Prasad.
- F. Gatti, X. Guitart, M. Masdeu, V. Rotger, Special values of triple-product p-adic L-functions and non-crystalline diagonal classes, J. Th. Nombres Bordeaux (Iwasawa 2019 special issue) 33 (2021), no. 3, part 1, 809-834.
- M. Roset, V. Rotger, V. Vatsal, On the L-invariant of the adjoint of a weight one modular form, J. London Math. Soc. 104 (2021) n. 1, 206--232
- O. Rivero, V. Rotger, Derived Beilinson-Flach elements and the arithmetic of the adjoint of a modular form, J. European Math. Soc. 23 (2021), no. 7, 2299--2335
- H. Darmon, V. Rotger, Stark-Heegner points and diagonal classes, Asterisque 434 (2022), 29--76.
- H. Darmon, V. Rotger, p-adic families of diagonal cycles, Asterisque 434 (2022), 1--28.
The two above papers are part of the collective volume with M. Bertolini, M. A. Seveso and R. Venerucci Heegner points, Stark-Heegner points and diagonal classes.
- O. Rivero, V. Rotger, Beilinson-Flach elements, Stark units and p-adic iterated integrals, Forum Math. 31 (2019), vol. 6, 1517--1532.
- H. Darmon, A. Lauder, V. Rotger, First order p-adic deformations of weight one newforms, in "L-functions and automorphic forms", Contributions in Mathematical and Computational Sciences 12 (2018), 39--80.
- M. Longo, V. Rotger, C. de Vera-Piquero, Heegner points on Hijigata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture, Publicacions Matematiques, 62 (2018), 355--396.
- D. Casazza, V. Rotger, On the elliptic Stark conjecture at primes of multiplicative reduction, Indiana Univ. Math. J., 68 (2019), 1233--1253.
- D. Casazza, V. Rotger, Stark points and Hida-Rankin p-adic L-functions, Ramanujar J. Math 45 (2018), 451--473.
- H. Darmon, V. Rotger, Elliptic curves of rank two and generalised Kato classes Research in Math. Sciences 3:27 (2016).
- H. Darmon, A. Lauder, V. Rotger, Overconvergent generalised eigenforms of weight one
and class fields of real quadratic fields, preprint 2014, Advances in Mathematics 283 (2015), 130--142.
- H. Darmon, A. Lauder, V. Rotger, Gross-Stark units and p-adic iterated integrals attached to modular forms of weight one, preprint 2014, Annales Math. Québec, 40 (2016), 325--354. Special issue marking the 60th birthday of Glenn Stevens.
- H. Darmon, A. Lauder, V. Rotger, Stark points and p-adic iterated integrals attached to modular forms of weight one, Forum of Mathematics, Pi (2015), Vol. 3, e8, 95 pages.
- H. Darmon, V. Rotger, Diagonal cycles and Euler systems II: The Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions Journal of the Amer. Math. Soc. 30 (2017), 601-672.
- M. Bertolini, H. Darmon, V. Rotger, Beilinson-Flach elements and Euler systems II: The Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions, J. Algebraic Geometry 24 (2015), 569--604.
- M. Bertolini, H. Darmon, V. Rotger, Beilinson-Flach elements and Euler systems I: syntomic regulators and p-adic Rankin L-series, J. Algebraic Geometry 24 (2015), 355--378.
- H. Darmon, V. Rotger, Diagonal cycles and Euler systems I: A p-adic Gross-Zagier formula, Annales Sc. École Normal Supérieure 47, n. 4 (2014), 779-832.
- M. Bertolini, F. Castella, H. Darmon, S. Dasgupta, K. Prasanna, V. Rotger, p-adic L-functions and Euler systems: a tale in two trilogies, Automorphic forms and Galois representations, London Math. Society Lecture Notes 414, (2014) 52-101.
- C. de Vera, V. Rotger, Galois representations over fields of moduli and rational points on Shimura curves, Canadian J. Math. 66 (2014), 1167-1200.
- F. Fite, K. Kedlaya, V. Rotger, A. Sutherland, Sato-Tate distributions and Galois endomorphism modules in genus 2, Compositio Mathematica 148, n. 5, (2012) 1390-1442.
- H. Darmon, M. Daub, S. Lichtenstein, V. Rotger, with an appendix by W. A. Stein, Algorithms for Chow-Heegner points via iterated integrals, Math. of Computation 84 (2015), 2505-2547.
- H. Darmon, V. Rotger, I. Sols, Iterated integrals, diagonal cycles and rational points on elliptic curves, Publ. Math. Besancon 2 (2012) 19-46.
- X. Guitart, V. Rotger, Y. Zhao, Almost totally complex points on elliptic curves, Transactions Amer. Math. Soc. 336 (2014), 2773-2802.
- H. Darmon, V. Rotger, Y. Zhao, The Birch and Swinnerton-Dyer conjecture for Q-curves and Oda's period relations, Geometry and Analysis of Automorphic forms of several variables, Proceedings of the International Symposium in Honor of Takayuki Oda on the Occasion of his 60th birthday, Series on Number Theory and its applications 7 World Scientific (2012) 1-40.
- M. Longo, V. Rotger, S. Vigni, Special values of L-functions and the arithmetic of Darmon points, Crelle's J. reine angew. Math. 684 (2013), 199-244.
- V. Rotger, M. A. Seveso, L-invariants and Darmon cycles attached to higher weight modular forms, J. European Math. Soc. 14 n. 6 (2012), 1955-1999.
- M. Longo, V. Rotger, S. Vigni, On rigid analytic uniformizations of Jacobians of Shimura curves, American J. Math. 134 n. 5 (2012), 1197--1246
- S. Molina, V. Rotger, Automorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes, Proc. American Math. Soc.142 (2014), 381-390.
- A. Kontogeorgis, V. Rotger, On the non-existence of exceptional
automorphisms on Shimura curves, Bull. London Math. Soc. 40 (2008) 363-374.
- V. Rotger, Which quaternion algebras act on a modular abelian variety?, Mathematical Research Letters 15 (2008), 251-263.
- A. Kontogeorgis, V. Rotger, On abelian automorphism groups of Mumford curves, Bull. London Math. Soc. 40 (2008) 353-362.
- J. González, V. Rotger, Non elliptic Shimura curves of genus one, J. Math. Soc. Japan 58:4 (2006), 927-948.
- N. Bruin, E. V. Flynn, J. González, V. Rotger, On finiteness conjectures for endomorphism algebras of abelian surfaces, Math. Proc. Camb. Phil. Soc. 141:3 (2006), 383-408.
- V. Rotger, A. Skorobogatov, A. Yafaev, Failure of the Hasse principle on Atkin-Lehner
quotients of Shimura curves over
 , Moscow Math. J. 5:2, (2005), 463-476.
- L. V. Dieulefait, V. Rotger, On abelian surfaces with potential quaternionic multiplication over , Bull. Belg. Math. Soc. 12:4, (2005) 617-624.
- J. González, J. Guàrdia, V. Rotger, Abelian surfaces of GL2-type as Jacobians, Acta Arithmetica 116 (2005), 263-287.
- S. Galbraith, V. Rotger, Easy Decision Diffie-Hellman groups, London Mathematical Society J. Comput. Math. 7 (2004), 201-218.
- V. Rotger, The field of moduli of the quaternionic multiplication on abelian varieties, International J. Math. M. Sc. 52 (2004), 2795-2808.
- L. V. Dieulefait, V. Rotger, The arithmetic of QM-abelian surfaces through their Galois representations, J. Algebra 281 (2004), 124-143.
- J. González, V. Rotger, Equations of Shimura curves of genus two, Intern. Res. Math. Not. 14 (2004), 661-674.
- V. Rotger, Modular Shimura varieties and forgetful maps, Trans. Amer. Math. Soc. 356 (2004), 1535-1550.
- V. Rotger, Shimura curves embedded in Igusas threefold, Modular curves and Abelian varieties, Progress in Mathematics, Birkhauser, 224 (2003), 263-273.
- V. Rotger, Quaternions, polarizations and class numbers, Crelle's J. reine angew. Math. 561 (2003),
177-197.
- V. Rotger, On the group of automorphisms of Shimura curves and applications, Compositio Mathematica 132 (2002), 229-241.
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