Tim Dokchitser
Heilbronn Chair in Arithmetic/Algebraic Geometry
University of Bristol Fry Building Woodland Road Bristol BS8 1UG
tel 0117 428 4878 (school manager)


Research
Most of my work concerns elliptic curves, the BirchSwinnertonDyer conjecture, Galois representations
and Lfunctions. All of my algorithms are in Magma:
Lfunctions,
Artin Representations, and
Galois Representations (new);
the original Paribased package ComputeL to compute special values of Lfunctions
is also
available
through William Stein's SAGE, and a database of
Artin representations is included in
LMFDB/Artin representations.
My most recent projects are
GroupNames.org
and
Regular models of curves.
Recent publications/preprints:
(arxiv)
Local Galois representations and Frobenius traces, with V. Dokchitser, preprint, January 2022
(arxiv)
Character formula for conjugacy classes in a coset, with V. Dokchitser, preprint, May 2021
(arxiv)
Parity reduction to 2Sylow, with V. Dokchitser, appendix to
V. Dokchitser, C. Maistret "Parity conjecture for abelian surfaces",
preprint, November 2019
(arxiv)
Tame torsion and the tame inverse Galois problem, with M. Bisatt, Math. Annalen 381(3) (2021), 14391453.
(abs,
pdf)
(arxiv)
Models of curves over discrete valuation rings, Duke Math. J. 170, no. 11 (2021), 25192574
(abs,
pdf)
(arxiv)
Tate module and bad reduction, with V. Dokchitser and A. Morgan, Proc. Amer. Math. Soc. 149 (2021), 13611372
(abs,
pdf)
(arxiv)
Arithmetic of hyperelliptic curves over local fields ("M2D2"), with V. Dokchitser, C. Maistret and A. Morgan,
Math. Ann. (2022), doi: 10.1007/s0020802102319y
(abs, pdf)
(arxiv)
3torsion and conductor of genus 2 curves, with C. Doris, Math. Comp. 88 (2019), 19131927
(abs,
pdf)
(arxiv)
Semistable types of hyperelliptic curves, with V. Dokchitser, C. Maistret and A. Morgan, Contemporary Math., vol. 724 (2019)
(arxiv)
Quotients of hyperelliptic curves and etale cohomology, with V. Dokchitser, Quaterly J. Math. 69, issue 2 (2018), 747768
(abs,
pdf)
(arxiv)
A positive proportion of hyperelliptic curves have odd/even 2Selmer rank, with V. Dokchitser, appendix to
M. Bhargava, B. H. Gross, X. Wang "Pencils of quadrics and the arithmetic of
hyperelliptic curves", J. Amer. Math. Soc. 30 (2017), 451493
(abs,
pdf)
(arxiv)
Rational representations and permutation representations of finite groups,
with A. Bartel, Math. Ann. 364, Issue 1 (2016), 539558
(abs)
(arxiv) Euler factors determine local Weil
representations, with V. Dokchitser, Crelle, Issue 717 (2016), 3546
(abs)
(arxiv)
Growth of Ш in towers for isogenous curves, with V. Dokchitser, Compositio Math. 151 (2015), 19812005
(abs);
(arxiv)
Local invariants of isogenous elliptic curves, with V. Dokchitser,
Trans. Amer. Math. Soc. 367 (2015), 43394358
(abs,
pdf);
(arxiv)
A remark on Tate's algorithm and Kodaira types, with V. Dokchitser, Acta
Arith. 160 (2013), 95100 (abs,
pdf)
(arxiv)
Noncommutative Iwasawa theory for modular forms,
with J. Coates, Z. Liang, W. Stein and R. Sujatha,
Proc. London Math. Soc. 107(3), 2013, 481516
(abs,
pdf)
(arxiv) Brauer relations in
finite groups II  quasielementary groups of order p^{a}q, with
A. Bartel, J. Group Theory 17, Issue 3 (2014), 381393.
(abs,
pdf)
(arxiv)
Surjectivity of mod 2^{n} representations of elliptic curves, with V. Dokchitser,
Math. Z., Vol. 272, Issue 34 (2012), 961964
(abs,
pdf)
(arxiv) Brauer relations in finite groups, with A. Bartel, J. Eur. Math. Soc. 17 (2015), 24732512
(arxiv) Identifying Frobenius
elements in Galois groups, with V. Dokchitser, Algebra and Number Theory 7 (2013), no. 6, 13251352
(abs)
(arxiv) Notes on the parity conjecture, September 2010,
CRM Barcelona Advanced Courses in Mathematics
"Elliptic Curves, Hilbert Modular Forms and Galois Deformations", Birkhauser, 2013
(publisher,
amazon)
(arxiv)
Solomon's induction in quasielementary groups, J. Group Theory 14 (2011), 4951
(abs)
(arxiv)
A note on the MordellWeil rank modulo n, with V. Dokchitser, J. Number Theory 131 (2011), 18331839
(abs)
(arxiv) Root numbers and parity
of ranks of elliptic curves, with V. Dokchitser,
Crelle, Issue 658 (2011), 3964
(abs)
(arxiv) A note on Larsen's conjecture and ranks of elliptic curves,
with V. Dokchitser, Bull. London Math. Soc. 41 no. 6 (2009), 10021008
(abs,
pdf)
(arxiv) Elliptic curves with all quadratic twists of positive rank, with V. Dokchitser, Acta Arith. 137 (2009), 193197
(abs)
(arxiv) Regulator constants and the parity conjecture, with V. Dokchitser, Invent. Math. 178, no. 1 (2009), 2371
(abs);
[Regulator constants  grouptheoretic version]
(arxiv) Quotients of functors of Artin rings,
Proc. Cam. Phil. Soc. 146 (2009), 531534
(abs)
(arxiv) Selfduality of Selmer groups, with V. Dokchitser,
Proc. Cam. Phil. Soc. 146 (2009), 257267 (pdf);
(arxiv) On the BirchSwinnertonDyer quotients modulo squares,
with V. Dokchitser, Annals of Math. 172 no. 1 (2010), 567596
(abs,
pdf)
[final version (Apr 2007) with the 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), 516524
(abs, pdf);
(arxiv)
Parity of ranks for elliptic curves with a cyclic isogeny, with V. Dokchitser, J. Number Theory 128 (2008), 662679
(abs,
pdf)
(arxiv) Ranks of elliptic curves in cubic extensions,
Acta Arith. 126 (2007), 357360 (abs,
pdf)
(arxiv) Computations in noncommutative Iwasawa theory, with V. Dokchitser
and appendix by J. Coates and R. Sujatha, Proc. London Math. Soc. (3) 94 (2006), 211272
(abs, pdf)
(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), 339373
(abs,
pdf)
(arxiv) LLL & ABC, J. Number Theory 107, No.1 (2004), 161167
(abs)
for additional algebraic ABC examples see
ABC conjecture home page
(arxiv)
Computing special values of motivic Lfunctions, Exper. Math. 13, No.2 (2004), 137149
(pdf)
My Ph.D. thesis (2000,
University of Utrecht, The Netherlands) is
``Deformations of pdivisible groups and pdescent on
elliptic curves''
This is a link to the thesis, and on the right is a link to the genealogy tree of my Ph.D. ancestors (light) and some of my Ph.D. relatives (dark).
Most of the data comes from the Mathematics Genealogy Project
at Minnesota State University.



Future/past events
Inverse Galois Problem
Park City online lectures, July 2630, 2021.
Algebraic Geometry
TCC graduate lecture course, with lecture notes, Autumn 2020.
Computational Number Theory
CMIHIMR Summer school, Bristol, 1728 June 2019
Curves and groups in families
Summer school,
Rennes, 1317 May 2019
Arithmetic of Curves
Workshop in Baskerville Hall, Wales, 1317 August 2018
Curves and Lfunctions
Summer school and workshop, ICTP Trieste, 28 August  8 September 2017
BSD Data @ Bristol
One day workshop, 28 March 2017
Galois Representations
TCC graduate lecture course, Autumn 2016
British Mathematical Colloquium
Bristol, 2124 March 2016
LMSCMI Summer school on Diophantine Equations
Baskerville Hall, 1420 September 2015
Elliptic curves, modular forms and Iwasawa theory
Conference in honour of the 70th birthday of John Coates, Cambridge, 2527 March 2015
Algebraic Geometry
TCC graduate lecture course, with lecture notes, Spring 2015.
2nd EU/US Summer School and Workshop on Automorphic Forms and Related Topics
Bristol, 30 June14 July 2014 
Lfunctions course lecture notes (3 lectures)
Average ranks of elliptic curves (after Bhargava and Shankar)
Short lecture course in Poznan, May 2014,
lecture notes by Zędrzej Garnek
LMS Regional meeting
"Arithmetic of
Lfunctions", Bristol, 13 October 2012
"Selmer Groups, Descent and Rank Distributions",
Warwick, 2428 September 2012
workshop home page; part of the
EPSRC Warwick Number Theory Symposium
School and Workshop on Computational Algebra and Number Theory, Trieste, 1829 June 2012
school website
BSD Summer school, Sardinia, 26 June3 July 2011
notes from all 3 courses by
Jim Brown
BSD Conference, Cambridge, 46 May, 2011
program, participants, talk notes
SAGE Days 22: Computing with elliptic curves, MSRI Berkeley, June 2010
program and videos
BirchSwinnertonDyer and Parity (Short course in CRM Barcelona, December 2009)
Course notes
and
references
Potential Modularity Day, 30 October 2009
program and videos