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Rational points on curves:

A *p*-adic and computational perspective

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September 24-28, 2012

Mathematical Institute, University of Oxford

This five day workshop was organised by Henri Darmon, Minhyong Kim, Alan Lauder and Jan Vonk, and supported by a grant from the European Research Council. It focussed on emerging methods for studying rational points on curves, especially from a p-adic and computational perspective. This focus included Stark-Heegner point constructions and methods from anabelian geometry, as well as related topics such as p-adic L-functions and p-adic modular forms. It took place in the Mathematical Institute, University of Oxford. Many participants stayed in the heart of Oxford at either Brasenose College or Hertford College.

Here is the programme for the workshop, and also a PDF file with a full list of abstracts.

Here are notes or slides for most of the talks:

- K. Prasanna:
*p*-Adic L-functions and the coniveau filtration on Chow groups notes - R. Pollack: Families of overconvergent modular symbols notes
- X. Guitart: Numerical computation of Stark-Heegner points in higher level slides
- J. Voight: Semi-arithmetic points notes
- S. Kobayashi: The
*p*-adic Gross-Zagier formula at supersingular primes slides - T. Gee: Patching functors and the cohomology of Shimura curves notes
- S. Hattori: Canonical subgroups via Breuil-Kisin modules notes
- Y. Taguchi: Rational torsions points of abelian varieties over a large extension of a local field notes
- S. Muller: A
*p*-adic BSD conjecture for modular abelian varieties slides - V. Di Proietto: On the
*p*-adic invariant cycles theorem notes - F. Baldassarri: Radius of convergence of
*p*-adic connections and the Berkovich ramification locus notes - G. Stevens: The Hodge-Tate sequence and overconvergent
*p*-adic modular sheaves notes - A. Iovita: An overconvergent Eichler-Shimura isomorphism notes
- M. Greenberg: Triple product
*p*-adic L-functions for balanced weights slides - A. Cadoret: l-adic representations of stale fundamental groups of curves notes
- G. Cornelissen: Recovering curves from L-series notes
- M. Bertolini:
*p*-adic Beilinson's formula for Rankin*p*-adic L-functions and applications notes - S. Dasgupta: Factorization of
*p*-adic Rankin L-series notes - D. Loeffler: Euler systems for Rankin-Selberg convolutions of modular forms notes
- P. Charollois: Eisenstein cocycles on GL_n and computation of
*p*-adic L-functions of totally real fields notes - H. Darmon:
*p*-adic iterated integrals and rational points on elliptic curves slides - A. Lauder: Efficient computation of Rankin
*p*-adic L-functions notes

Here is a list of participants:

J. Balakrishnan (Harvard), F. Baldassarri (Padova), M. Bertolini (Milan), Anna Cadoret (EP),
P. Charollois (Paris VI), B. Chiarellotto (Padova), G. Cornelissen (Utrecht), H. Darmon (McGill)
S. Dasgupta (UCSC), M. Daub (Berkeley), T. Gee (Imperial),
M. Greenberg (Calgary), X. Guitart (UP Catalunya/MPIM), S. Hattori (Kyushu), A. Iovita (Concordia/Padova),
V. Karemakers (Utrecht), K. Kedlaya (MIT), A. Langer (Exeter),
M. Lettington (Cardiff), D. Loeffler (Warwick), M. Longo (Padova)
S. Kobayashi (Tohoku), M. Kurihara (Keio), A. Lauder (Oxford/Kyushu), K. Morita (Hokkaido), Steffen Muller (Hamburg), J. Park (POSTECH), B. Perrin-Riou (Orsay), R. Pollack (Boston)
K. Prasanna (Michigan), V. Di Proietto (Tokyo), G. Rosso (KU Leuven),
V. Rotger (UP Catalunya),
M. Seveso (Milan), A. Shiho (Tokyo), G. Stevens (Boston),
M. Stoll (Bayreuth), Y. Taguchi (Kyushu), J. Tuitman (Oxford),
J. Van Order (EPFL), R. Venerucci (Milan), J. Voight (Vermont),
J. Vonk (Oxford), G. Wiese (Luxembourg), A. Wiles (Oxford),
S. Zerbes (UCL).

Here are two photographs of the participants: one, two

The workshop was open to all, with limited financial support available aimed at graduate students and postdoctoral researchers.