Publications of Massimo Bertolini


Research articles

  • M. Bertolini, G. Canuto, Good reduction of elliptic curves over Q(cuberoot{2}), Archiv der Mathematik 50 (1988) 42-50.

  • M. Bertolini, H. Darmon, Kolyvagin's descent and Mordell-Weil groups over ring class fields, Journal für die reine und angewandte Mathematik 412 (1990) pp. 63-74.

  • M. Bertolini, Iwasawa theory, L-functions and Heegner points, PhD Thesis, Columbia University (1992).

  • M. Bertolini, An annihilator for the p-Selmer group by means of Heegner points, Atti Acc. Naz. Lincei, Classe di Sc. Fis., Mat. e Nat., Rendiconti Lincei, Mat. e Appl., Serie 9, Vol. 5 , Fasc. 2 (1994) 129-140.

  • M. Bertolini, H. Darmon, Derived heights and generalized Mazur-Tate regulators, Duke Math. Journal 76 (1994) 75-111.

  • M. Bertolini, Selmer groups and Heegner points in anticyclotomic Zp-extensions, Compositio Math. 99, n. 2 (1995) 153-182.

  • M. Bertolini, H. Darmon, Derived p-adic heights, American Journal of Math. 117 (1995) 1517-1554.

  • M. Bertolini, p-adic heights and p-adic L-functions, Atti I Incontro Italiano di Teoria dei Numeri, Rend. Sem. Mat. - Univ. Pol. Torino, Vol. 53, N. 3 (1995) 193-206.

  • M. Bertolini, H. Darmon, Heegner points on Mumford-Tate curves, Inventiones Math. 126, Fasc. 3 (1996) 413-453.

  • M. Bertolini, Growth of Mordell-Weil groups in anticyclotomic towers, Proc. Symp. Arithmetic Geom., F. Catanese, ed., Arithmetic Geometry, Symposia Mathematica Vol. XXXVII, Cambridge Univ. Press (1997) 23-44.

  • M. Bertolini, Elliptic curves and special values of L-series, Proc. XIX Journées Arith., Collectanea Mathematica Vol. XLVIII, Fasc. 1-2 (1997) 31-39.

  • M. Bertolini, H. Darmon, A rigid analytic Gross-Zagier formula and arithmetic applications (With an appendix by B. Edixhoven), Annals of Math. 146 (1997) 111-147.

  • M. Bertolini, H. Darmon, Heegner points,p-adic L-functions, and the Cerednik-Drinfeld uniformization, Inventiones Math. 131 (1998) 453-491.

  • M. Bertolini, H. Darmon, Non-triviality of families of Heegner points and ranks of Selmer groups over anticyclotomic towers, J. Ramanujan Math. Soc. 13 (1998) 15-24.

  • M. Bertolini, H. Darmon, Euler systems and Jochnowitz congruences, American Journal Math. 121, n. 2 (1999) 259-281.

  • M. Bertolini, H. Darmon, p-adic periods, p-adic L-functions, and the p-adic uniformization of Shimura curves, Duke Math. Journal 98, no. 2 (1999) 305-334.

  • M. Bertolini, Iwasawa theory for elliptic curves over imaginary quadratic fields, Proceedings XXI Journées Arithmétiques, J. Th. Nombres de Bordeaux 13, Fasc. 1 (2001) 1-25.

  • M. Bertolini, H. Darmon, The p-adic L-functions of modular elliptic curves, "Mathematics Unlimited -- 2001 and Beyond", Springer Verlag (2001) 109-170.

  • M. Bertolini, H. Darmon, A. Iovita, M. Spiess, Teitelbaum's exceptional zero conjecture in the anticyclotomic setting, American J. Math. 124 (2002) 411-449.

  • M. Bertolini, H. Darmon, P. Green, Periods and points attached to quadratic algebras, MSRI Publ. 49, Cambridge Univ. Press, 323-367, 2004.

  • M. Bertolini, H. Darmon, A Birch and Swinnerton-Dyer conjecture for the Mazur-Tate circle pairing, Duke Mathematical Journal 122 (2004) n. 1, 181-204.

  • M. Bertolini, H. Darmon, Iwasawa's Main Conjecture for elliptic curves over anticyclotomic Zp-extensions, Annals of Math. (2) 162 (2005), no. 1, 1-64.

  • M. Bertolini, H. Darmon, Hida families and rational points on elliptic curves, Inventiones Math. 168 (2007), no. 2, 371-431.

  • M. Bertolini, H. Darmon, S. Dasgupta, "L-functions and Galois representations", London Mathematical Society Lecture Note Series 320, Cambridge Univ. Press, 1-23, 2007.

  • M. Bertolini, H. Darmon, Rationality of Stark-Heegner points over genus fields of real quadratic fields, Annals of Math. 170 (2009), 287-313.

  • M. Bertolini, H. Darmon, A. Iovita, Families of automorphic forms on definite quaternion algebras and Teitelbaum's conjecture, Astérisque 331 (2010), 29-64.

  • M. Bertolini, H. Darmon, K. Prasanna, p-adic Rankin L-series and rational points on CM elliptic curves , Pacific J. Math. 260, No. 2, Jonathan Rogawski Memorial Volume, (2012) 261-303.

  • M. Bertolini, H. Darmon, K. Prasanna, Generalised Heegner cycles and p-adic Rankin L-series (With an appendix by Brian Conrad), Duke Math. J. 162 No. 6 (2013), 1033-1148.

  • M. Bertolini, H. Darmon, K. Prasanna, Chow-Heegner points on CM elliptic curves and values of p-adic L-functions , Int. Math. Res. Not. IMRN 2014, no. 3, 745-793.

  • M. Bertolini, H. Darmon, Kato's Euler system and rational points on elliptic curves I: A p-adic Beilinson formula , Israel J. Math. 199 (2014) n. 1, 163-188.

  • M. Bertolini, H. Darmon, V. Rotger, Beilinson-Flach elements and Euler systems I: Syntomic regulators and p-adic Rankin L-series , J. Alg. Geometry 24 (2015) no. 2, 355-378.

  • M. Bertolini, H. Darmon, V. Rotger, Beilinson-Flach elements and Euler systems II: The Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-series , J. Alg. Geometry 24 (2015) no. 3, 569-604.

  • A. Berti, M. Bertolini, R. Venerucci, Congruences between modular forms and the Birch and Swinnerton-Dyer conjecture , "Elliptic curves, modular forms and Iwasawa theory'', John Coates' 70th Birthday Proceedings, Springer Proceeedings in Mathematics and Statistics Vol. 188 (2017) 1-31.

  • M. Bertolini, H. Darmon, K. Prasanna, p-adic L-functions and the coniveau filtration on Chow groups (With an appendix by Brian Conrad), J. Reine Angew. Math. 731 (2017), 21–86.

  • M. Bertolini, M. Seveso, R. Venerucci, Diagonal classes and the Bloch-Kato conjecture , Christopher Deninger 60th Birthday Proceedings, Muenster Journal of Mathematics 13 (2020) no. 2, 317-352.

  • M. Bertolini, H. Darmon, D. Lilienfeldt, K. Prasanna, Generalised Heegner cycles and the complex Abel-Jacobi map , Mathematische Zeitschrift (2021) 298(1), 385-418.

  • M. Bertolini, H. Darmon, R. Venerucci, Heegner points and Beilinson-Kato elements: A conjecture of Perrin-Riou , Advances in Mathematics 398 (2022), Paper no. 108172, 50pp.

  • M. Bertolini, M. Seveso, R. Venerucci, Reciprocity laws for balanced diagonal classes , Astérisque 434 (2022) 77-174, Volume edited with H. Darmon and V. Rotger "Heegner points, Stark-Heegner points and diagonal classes" .

  • M. Bertolini, M. Seveso, R. Venerucci, Erratum to Reciprocity laws for balanced diagonal classes.

  • M. Bertolini, M. Seveso, R. Venerucci, Balanced diagonal classes and rational points on elliptic curves , Astérisque 434 (2022) 175-201, Volume edited with H. Darmon and V. Rotger "Heegner points, Stark-Heegner points and diagonal classes" .

  • M. Bertolini, M. Seveso, R. Venerucci, On p-adic analogues of the Birch and Swinnerton-Dyer conjecture for Garrett L-functions, (2022) submitted.

  • M. Bertolini, M. Seveso, R. Venerucci, On exceptional zeros of Garrett-Hida p-adic L-functions, (2021) Volume in honour of B. Perrin-Riou, Annales Math. du Québec, to appear.

  • M. Bertolini, M. Seveso, R. Venerucci, Heegner points and exceptional zeros of Garrett p-adic L-functions, (2021) Milan Journal of Mathematics, to appear.

Expository articles

  • M. Bertolini, G. Canuto, La congettura di Shimura-Taniyama-Weil, Boll. U.M.I. (7), 10-A (1996) 213-247.

  • M. Bertolini, L'Ultimo Teorema di Fermat, L'Ins. Mat. Sc. Int., vol. 19B, n. 3 (1996) 236-247.

  • M. Bertolini, Curve ellittiche e numeri congruenti, Archimede 1 (2001) 32-45.

  • M. Bertolini, L'ultimo teorema di Fermat e alcuni aspetti della Teoria dei numeri nell'ultimo decennio, Enciclopedia del Novecento "Treccani", Supplemento III, volume A-G (2004) 487-493.

  • M. Bertolini, L'Ultimo Teorema di Fermat, "La matematica", volume 2, Einaudi (2008) 313-334.

  • M. Bertolini, Report on the Birch and Swinnerton-Dyer conjecture, Proceedings of the Symposium "Advances in Number Theory and Geometry", International School and Workshop on "150 years of Riemann Hypothesis" (director E. Bombieri), Milan Journal of Mathematics 78 (2010) 153-178.

  • M. Bertolini, Campi di numeri, Rappresentazioni galoisiane, Forme modulari , Congettura di Birch e Swinnerton-Dyer, voci della Enciclopedia della Scienza e della Tecnica "Treccani".

  • M. Bertolini, Regulators, L-functions and rational points, Proceedings of the XIX Congress of Unione Matematica Italiana, Bollettino UMI, Serie IX, Vol. VI, N. 1 (2013) 191-204.

  • M. Bertolini, F. Castella, H. Darmon, S. Dasgupta, K. Prasanna, V. Rotger, p-adic L-functions and Euler systems: a tale in two trilogies, Proceedings of the Durham Symposium on Galois representations and L-functions, Automorphic Forms and Galois Representations, Vol. 1, F. Diamond, P.L. Kassaei, M. Kim, editors, LMS Lecture Note Series 414, Cambridge University Press (2014) 52-101.

  • M. Bertolini, Kubische Kurven - von der Antike bis heute , Unikate, Heft 53, 2018.