39 citations · 74 across the 9 of their papers we have counts for
10 papers
Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields
D. V. Osipov, A. N. Parshin
We study a natural action of the Heisenberg group of integer unipotent matrices of the third order on distribution space of a two-dimensional local field for a flag on a two-dimens…
Harmonic analysis and the Riemann-Roch theorem
D. V. Osipov, A. N. Parshin
This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from these papers and two-dimensional ad…
Representations of Higher Adelic Groups and Arithmetic
A. N. Parshin
We discuss the following topics: n-dimensional local fields and adelic groups; harmonic analysis on local fields and adelic groups for two-dimensional schemes (function spaces, Fou…
Notes on the Poisson formula
A. N. Parshin
These notes are a part of my lectures on representations of adelic groups attached to two-dimensional schemes. They contain a study of the one-dimensional case as a preliminary ste…
Finiteness Problems in Diophantine Geometry
Yuri G. Zarhin, Alexey N. Parshin
This survey contains an exposition of ideas and results related to Faltings' proof of the conjectures of Shafarevich, Tate and Mordell. This paper originally appeared in 1986 as an…
Numbers as functions: the development of an idea in the Moscow school of algebraic geometry
A. N. Parshin
This is expanded text of a lecture delivered by the author at the conference "Matériaux pour l'Histoire des Mathématiques au XXème siècle", which took place in Nice in January 1996…