39 citations · 74 across the 9 of their papers we have counts for
5 papers · 1 filter
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…
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…
Harmonic analysis on local fields and adelic spaces II
D. V. Osipov, A. N. Parshin
This paper is the second part of arXiv:0707.1766. We develope harmonic analysis in some categories of filtered abelian groups and vector spaces over the fields R or C. These catego…
Adelic Lefschetz formula for the action of a one-dimensional torus
Sergey Gorchinskiy, Alexey Parshin
There exists a well-known Lefschetz formula for the number of fixed points in algebraic topology. In algebraic geometry, there exist cohomologies of coherent sheaves. It is natural…
On a Ring of Formal Pseudo-differential Operators
A. N. Parshin
We study the notion of non-commumative higher dimensional local fields. A simplest example is the ring P of formal pseudo- differential operators. As an application we extend the K…