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 Professor and a Royal Society University Research Fellow at University College London.

Mathematical stuff (arxiv):

A note on hyperelliptic curves with ordinary reduction over 2-adic fields, with A. Morgan.

Local Galois representations and Frobenius traces, with T. Dokchitser.

Character formula for conjugacy classes in a coset, with T. Dokchitser.

A user's guide to the local arithmetic of hyperelliptic curves, with A. Best, A. Betts, M. Bisatt, R. van Bommel, O. Faraggi, S. Kunzweiler, C. Maistret, A. Morgan, S. Muselli, S. Nowell,

to appear in Bull. London Math. Soc.

Parity conjecture for abelian surfaces, with C. Maistret (appendices by A. Morgan, T. Dokchitser, V. Dokchitser).

On a BSD-type formula for L-values of Artin twists of elliptic curves, with R. Evans, H. Wiersema.

J. Reine Angew. Math. 773 (2021), 199-230.

Tate module and bad reduction, with T. Dokchitser, A. Morgan.

Proc. Amer. Math. Soc. 149 (2021), 1361-1372.

Arithmetic of hyperelliptic curves over local fields, with T. Dokchitser, C. Maistret, A. Morgan.

to appear in Math. Annalen.

Constructing hyperelliptic curves with surjective Galois representations, with S. Anni,

Trans. Amer. Math. Soc. 373 (2020), no. 2, 1477-1500.

Semistable types of hyperelliptic curves, with T. Dokchitser, C. Maistret, A. Morgan,

in Algebraic Curves and their Applications, L. Beshaj, T. Shaska (editors), Contemporary Math.

On the Birch-Swinnerton-Dyer conjecture and Schur indices, with M. Bisatt,

Bull. London Math. Soc. 50 (2018) 1027-1034.

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

Quarterly Journal of Mathematics (2) 69 (2018) 747-768.

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

Variation of Tamagawa numbers of semistable abelian varieties in field extensions , with L. A. Betts,

Math. Proc. Cambridge Philos. Soc., 1-35.

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

appendix to
A positive proportion of hyperelliptic curves over Q have no point over any odd degree extension, by M. Bhargava, B. H. Gross and X. Wang,

J. Amer. Math. Soc. 30 (2017), 451-493.

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

Compositio Mathematica 151 (2015), 1981-2005.

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,

Trans. Amer. Math. Soc. 367 (2015), 4339-4358.

Euler factors determine local Weil representations, with T. Dokchitser,

J. Reine Angew. Math. 717 (2016), 35-46.

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

Root numbers of non-abelian twists of elliptic curves (appendix by T. Fisher),

Proc. London Math. Soc. (3) 91 (2005), 300-324

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