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 at University College London and the current Director of the London School of Geometry and Number Theory (LSGNT).
Mathematical stuff (arxiv):
Reduction of plane quartics and Cayley octads, with R. van Bommel, J. Docking, R. Lercier, E. Lorenzo Garcia.
Root numbers and parity phenomena, with L. Cowland Kellock.
Bull. London Math. Soc. (online version of record).
Parity of ranks of Jacobians of curves, with H. Green, A. Konstantinou, A. Morgan.
A note on hyperelliptic curves with ordinary reduction over 2-adic fields, with A. Morgan.
J. Number Theory 244 (2023), 264-278.
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,
Bull. London Math. Soc. 54 (2022), no. 3, 825-867.
On the parity conjecture for abelian surfaces, with C. Maistret (appendices by A. Morgan, T. Dokchitser, V. Dokchitser).
Proc. London Math. Soc. (3) 127 (2023), 295-365.
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.
Math. Annalen 385, 1213-1322 (2023).
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. (3) 166 (2019), 487-521.
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 2n 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).