Welcome to Vladimir Dokchitser's home page.

This page is still under construction, and will remain such until an unspecified
future date.

I am a Royal Society University Research Fellow at the Warwick Mathematics Institute. .

Interests: Several.

Other Interests: Many.

Some mathematical stuff:

Quotients of hyperelliptic curves and etale cohomology, with T. Dokchitser

l-adic representations and their associated invariants, with S. Anni (graduate school lecture notes)

Finite quotients of Z[C_n]-lattices and Tamagawa numbers of semistable abelian varieties , with L. A. Betts

A positive proportion of hyperelliptic curves have odd/even 2-Selmer rank, with T. Dokchitser

appendix to
Pencils of quadrics and the arithmetic of hyperelliptic curves, by M. Bhargava, B. H. Gross and X. Wang,

to appear in J. Amer. Math. Soc.

Growth of Sha in towers for isogenous curves, with T.Dokchitser

to appear in Compositio Math.

A remark on Tate's algorithm and Kodaira types, with T.Dokchitser

Acta Arith. 160 (2013), 95-100

Local invariants of isogenous elliptic curves, with T.Dokchitser

to appear in Trans. Amer. Math. Soc.

Euler factors determine local Weil representations, with T.Dokchitser

to appear in J. Reine Angew. Math.

Surjectivity of mod 2^{n} representations of elliptic curves, with T.Dokchitser

Math. Z. 272, Issue 3-4 (2012), 961-964

Identifying Frobenius elements in Galois groups, with T.Dokchitser,

Algebra and Number Theory 7 (2013), no. 6, 1325-1352

A note on the Mordell-Weil rank modulo n, with T.Dokchitser,

J. Number Theory 131 (2011), 1833-1839

Root numbers and parity of ranks of elliptic curves, with T. Dokchitser,

J. Reine Angew. Math. 658 (2011), 39-64

A note on Larsen's conjecture and ranks of elliptic curves, with T. Dokchitser,

Bull. London Math. Soc. 41, no. 6 (2009), 1002-1008

Elliptic curves with all quadratic twists of positive rank, with T. Dokchitser,

Acta Arith. 137 (2009), 193-197

Regulator constants and the parity conjecture, with T. Dokchitser,

Invent. Math. 178, no. 1 (2009), 23-73

Self-duality of Selmer groups, with T. Dokchitser,

Math. Proc. Cambridge Philos. Soc. 146 (2009), 257-267

Root numbers of elliptic curves in residue characteristic 2, with T. Dokchitser,

Bull. London Math. Soc. 40 (2008), 516-524

On the
Birch-Swinnerton-Dyer quotients modulo squares, with T. Dokchitser,

Annals of Math. 172, no. 1 (2010), 567-596

Parity of ranks for
elliptic curves with a cyclic isogeny, with T. Dokchitser,

J. Number Theory 128 (2008), 662-679

Computations in non-commutative
Iwasawa theory, with T. Dokchitser

(appendix by J. Coates and R. Sujatha),
Proc. London Math. Soc. (3) 94 (2006) 211-272

Algebraicity of L-values
for elliptic curves in a false Tate curve tower, with Th. Bouganis,

Math. Proc. Cambridge Philos. Soc. 142 (2007) 2, 193-204

L-functions of non-abelian twists of
elliptic curves (Ph.D. thesis, August 2005)

Root
numbers of non-abelian twists of elliptic curves

(appendix by T. Fisher), Proc. London Math. Soc. (3) 91
(2005), 300-324

Computing
L-values of twists of elliptic curves
and numerical
data (essay, January 2004)

On
the 6-colour conjecture in R^3
(preprint, August 2003)

Other works of art:

John
Coates' mathematical family tree

2003
Part IV Examination Paper