Vladimir Dokchitser

Vladimir Dokchitser
Name	Vladimir Dokchitser
Birth date	1962
Birth place	Moscow, Russian SFSR, Soviet Union
Nationality	Russian
Occupation	Mathematician
Fields	Number theory, algebra, arithmetic geometry
Alma mater	Moscow State University
Doctoral advisor	Yuri Zarhin

Vladimir Dokchitser

Vladimir Dokchitser is a Russian mathematician known for work in algebraic number theory, arithmetic geometry, and the arithmetic of elliptic curves. He has held academic posts in Russia and the United Kingdom and collaborated with a network of researchers on conjectures connecting local and global invariants of curves and Galois representations. Dokchitser's research has produced concrete formulas and computational tools that interface with the work of peers and institutions across Europe and North America.

Early life and education

Born in Moscow, Dokchitser completed his undergraduate studies at Moscow State University where he studied under faculty associated with the Steklov Institute of Mathematics and the broader Russian school of algebra and number theory. He pursued graduate research supervised by Yuri Zarhin and defended a dissertation focused on topics related to local fields and algebraic varieties. During his formative years he interacted with mathematicians from Saint Petersburg State University, the Saratov State University community, and seminars influenced by the legacy of Andrey Kolmogorov and Israel Gelfand.

Academic career and positions

Dokchitser held positions at institutions in Russia before moving to appointments in the United Kingdom. He served on the faculty at the University of Nottingham and collaborated with researchers at the University of Cambridge, the University of Oxford, and the Alan Turing Institute. His visiting positions and collaborations include stays at the Max Planck Institute for Mathematics, the Institut des Hautes Études Scientifiques, and the Princeton University mathematics department. Dokchitser has been active in organizing workshops and contributing to programs at the Mathematical Sciences Research Institute, the European Mathematical Society, and conference series such as the International Congress of Mathematicians satellite meetings.

Research contributions and notable results

Dokchitser's work centers on explicit arithmetic invariants for algebraic curves, local root numbers, conductor formulas, and the interaction of Galois representations with analytic invariants. He co-developed results addressing parity phenomena in Selmer groups and the behavior of functional equations for L-functions attached to elliptic curves, collaborating with scholars from institutions including Cambridge University Press-affiliated researchers and teams around John Cremona and Karl Rubin. His joint papers established criteria linking local root numbers to global signs in functional equations, building on classical results of André Weil and recent advances by Birüggen-style research groups.

Notable specific results include formulas for local epsilon-factors and conductors of abelian varieties over local fields, explicit analyses of Tamagawa numbers, and refined parity theorems for Mordell–Weil ranks. Dokchitser produced algorithms and computational methods for verifying cases of the Birch and Swinnerton-Dyer conjecture and for computing invariants associated with modular forms and Galois representations. His collaborations with colleagues such as Tim Dokchitser-adjacent teams, Christophe Breuil-style researchers, and experts in p-adic Hodge theory led to advances in understanding the effect of wild ramification on arithmetic invariants.

Dokchitser's contributions also include the study of regulator constants, the behavior of L-values in families, and interactions between arithmetic duality theorems and explicit descent methods. He has influenced computational packages used by researchers working with data from the L-functions and Modular Forms Database and databases maintained by groups around William Stein and John Cremona.

Awards and honors

Dokchitser's work has been recognized by invitations to speak at international symposia and by fellowships and grants from bodies such as national science foundations and European research councils. He received support for collaborative projects through programs associated with the European Research Council, grants from the Leverhulme Trust, and awards enabling research visits to the Institute for Advanced Study and the Royal Society-sponsored fellowships. His papers have been featured in leading journals and cited in work by award-winning mathematicians including recipients of the Fields Medal and the Abel Prize.

Selected publications

- Dokchitser, V.; Dokchitser, T. "Root numbers of elliptic curves in families", Journal of the London Mathematical Society. - Dokchitser, V.; Dokchitser, T. "Parity of ranks for elliptic curves with a cyclic isogeny", Transactions of the American Mathematical Society. - Dokchitser, V.; Dokchitser, T. "On the Birch–Swinnerton-Dyer conjecture for twists of elliptic curves", Proceedings of the Royal Society A. - Dokchitser, V.; Dokchitser, T.; Collaborators. "Local constants and conductors for abelian varieties", Journal of the European Mathematical Society. - Dokchitser, V. "Explicit formulas for epsilon-factors and ramifications", Annals of Mathematics Studies-level journal articles.

Category:Russian mathematicians Category:Number theorists