| DPMMS | Robinson | Research | Part III Essay |
Number theory seminar |
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Potential Modularity Day |
Tim DokchitserRoyal Society University Research Fellow
Dept of Pure Maths and Math Statistics Robinson College, Cambridge, CB3 9AN DPMMS office C0.11 |
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Most of my work concerns elliptic curves and the "standard conjectures" for L-functions associated to arithmetic varieties. For my algorithms to compute special values of these L-functions see ComputeL (Pari-based), Magma (starting from V2.12, July 2005, see L-functions chapter) and W. Stein's SAGE
Recent publications/preprints:
(arxiv)
A note on the Mordell-Weil rank modulo n, with V. Dokchitser, preprint, October 2009
(arxiv) Root numbers and parity of ranks of elliptic curves, with V. Dokchitser, preprint, June 2009
(arxiv) A note on Larsen's conjecture and ranks of elliptic curves,
with V. Dokchitser, Bull. London Math. Soc. 41 no. 6 (2009), 1002-1008
(abs,
pdf)
(arxiv) Elliptic curves with all quadratic twists of positive rank, with V. Dokchitser, Acta Arith. 137 (2009), 193-197
(journal)
(arxiv) Regulator constants and the parity conjecture, with V. Dokchitser, Invent. Math. 178, no. 1 (2009), 23-71
(journal)
[Regulator constants - group-theoretic version]
(arxiv) Quotients of functors of Artin rings,
Proc. Cam. Phil. Soc. 146 (2009), 531-534
(abs,
pdf)
(arxiv) Self-duality of Selmer groups, with V. Dokchitser,
Proc. Cam. Phil. Soc. 146 (2009), 257-267 (pdf)
(arxiv) On the Birch-Swinnerton-Dyer quotients modulo squares, with V. Dokchitser, to appear in Annals of Math.
[final
journal version with a proof of the Parity Conjecture for Selmer ranks over Q]
(arxiv) Root numbers of elliptic curves in residue characteristic 2, with V.
Dokchitser
Bull. London Math. Soc. 40 (2008), 516-524
(abs, pdf)
(arxiv) Parity of ranks for elliptic curves with a cyclic isogeny, with V. Dokchitser, J. Number Theory 128 (2008), 662-679
(pdf)
(arxiv) Ranks of elliptic curves in cubic extensions,
Acta Arith. 126 (2007), 357-360
(arxiv) Computations in non-commutative Iwasawa theory, with V. Dokchitser
and appendix by J. Coates and R. Sujatha, Proc. London Math. Soc. (3) 94 (2006), 211-272
(arxiv) Numerical verification of Beilinson's conjecture for K2 of hyperelliptic curves,
with R. de Jeu and D. Zagier
Compositio Math. 142, Issue 02 (2006), 339-373
(pdf)
(arxiv) LLL & ABC, J. Number Theory 107, No.1 (2004), 161-167
(pdf)
for additional algebraic ABC examples see
ABC conjecture home page
(arxiv)
Computing special values of motivic L-functions, Exper. Math. 13, No.2 (2004), 137-149
(pdf)
| My Ph.D. thesis (2000,
University of Utrecht, The Netherlands) is
``Deformations of p-divisible groups and p-descent on elliptic curves'' This is a link to the
thesis, and on the right is
a link to the genealogy tree |
My Ph.D. genealogy tree |
Abelian varieties over finite fields
Example sheet 1: plane curves for 30/1
Example sheet 2: isogenies for 13/2
Exercise sheet 1
Exercise sheet 2
Exercise sheet 3
Exercise sheet 4