Arithmetic of Euler systems

2015, Aug 22 -- Aug 30

Organizers:
X. Guitart (U. Barcelona)
M. Masdeu (Warwick U.)

Main References

[BD1] Massimo Bertolini and Henri Darmon, Kato's Euler system and rational points on elliptic curves I: A p-adic Beilinson formula. Israel Journal of Mathematics 199, Issue 1, January 2014, 163-188.

[BDR1] Massimo Bertolini, Henri Darmon, Victor Rotger, Beilinson - Flach elements and Euler systems I: syntomic regulators and p-adic Rankin L-series, J. Algebraic Geom. 24 (2015), 355-378.

[BDR2] Massimo Bertolini, Henri Darmon, and Victor Rotger, Beilinson - Flach elements and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions, preprint.

[DR1] Henri Darmon and Victor Rotger, Diagonal cycles and Euler systems I: a p-adic Gross-Zagier formula, Annales Scientifiques de l'Ecole Normale Supérieure, 47 no. 4 (2014) 779-832

[DR2] Henri Darmon and Victor Rotger, Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-series, preprint.

[Kato] Kazuya Kato, P-adic Hodge theory and values of zeta functions of modular forms, Asterisque 295 (2004), ix, 117-290, Cohomologies p-adiques et applications arithmetiques. III.

[KLZ1] Guido Kings, David Loeffler, and Sarah Livia Zerbes, Rankin-Eisenstein classes for modular forms, preprint, 2015, arXiv:1501.03289.

[KLZ2] Guido Kings, David Loeffler, and Sarah Livia Zerbes, Rankin-Eisenstein classes and explicit reciprocity laws, preprint, 2015, arxiv:1503.02888

[LLZ1] Antonio Lei, David Loeffler, and Sarah Livia Zerbes, Euler systems for Rankin-Selberg convolutions of modular forms, Ann. of Math. (2) 180 (2014), no. 2, 653-771.

Other References

[BaK] Kenichi Bannai and Guido Kings, p-adic elliptic polylogarithm, p-adic Eisenstein series and Katz measure, Amer. J. Math. 132 (2010), no. 6, 1609-1654.

[Berger] Laurent Berger, Bloch and Kato's exponential map: three explicit formulas, Doc. Math. Extra Vol. 3 (2003), 99-129, Kazuya Kato's Fiftieth Birthday.

[BCDDPR] Massimo Bertolini, Francesc Castella, Henri Darmon, Samit Dasgupta, Kartik Prasanna, and Victor Rotger, p-adic L-functions and Euler systems: a tale in two trilogies, in Automorphic forms and Galois representations, London Mathematical Society Lecture Notes Series 414.

[Bes1] Amnon Besser, Syntomic regulators and p-adic integration. I. Rigid syntomic regulators, Israel J. Math. 120 (2000), no. 1, 291-334.

[Bes2] Amnon Besser, A generalization of Coleman's p-adic integration theory, Invent. Math. 142 (2000), no. 2, 397-434.

[Bes3] Amnon Besser, On the syntomic regulator for K1 of a surface, Israel J. Math. 190 (2012), no. 1, 29-66.

[BLZ] Amnon Besser, David Loeffler, and Sarah Livia Zerbes, Finite polynomial cohomology for general varieties, P-adic variation in number theory (Glenn Stevens 60th birthday proceedings), 2015, arXiv:1405.7527.

[DeM] Frederic Deglise and Nicola Mazzari, The rigid syntomic ring spectrum, J. Inst. Math. Jussieu (to appear).

[Kings] Guido Kings, Eisenstein classes, elliptic Soule elements and the l-adic elliptic polylogarithm, The Bloch-Kato conjecture for the Riemann zeta function (John Coates, Anantharam Raghuram, Anupam Saikia, and Ramdorai Sujatha, eds.), London Math. Soc. Lecture Note Ser., vol. 418, Cambridge Univ. Press, 2015.

[LLZ0] Antonio Lei, David Loeffler, and Sarah Livia Zerbes, Coleman maps and the p-adic regulator, Algebra & Number Theory 5 (2011), no. 8, 1095-1131

[LLZ2] Antonio Lei, David Loeffler, and Sarah Livia Zerbes, Euler systems for modular forms over imaginary quadratic fields, Compos. Math. (2015), to appear, arXiv:1311.0175

[Ohta] Masami Ohta, Ordinary p-adic etale cohomology groups attached to towers of elliptic modular curves. II, Math. Ann. 318 (2000), no. 3, 557-583

[Scholl] A.J. Scholl, An introduction to Kato's Euler systems, Galois representations in arithmetic algebraic geometry, ed. A. J. Scholl and R. L. Taylor. Cambridge University Press 1998, 379-460