Related papers: The Work of John Tate

The 75th anniversary of Turing's seminal paper and his centennial year anniversary occur in 2011 and 2012, respectively. It is natural to review and assess Turing's contributions in diverse fields in the light of new developments that his…

Problems for evaluation and impact of published scientific works and their authors are discussed. The role of citations in this process is pointed out. Different bibliometric indicators are reviewed in this connection and ways for…

This short note introduces a formal system of truth and paradoxicality, outlining the main motivation, and proving its $\omega$-consistency. The system is called TP, for 'Truth and Paradoxicality'.

Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.

This paper shows that the main features of Turing's thesis derived from those of the expression system (Turing machines) it inaugures, and in particular its conformity. The notions of inaugural statements and texts are defined and…

The objective of this article is to give an introduction to p-adic analysis along the lines of Tate's thesis, as well as incorporating material of a more recent vintage, for example Weil groups.

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…

Brief Description: The book provides a unique highly self-contained text introducing the reader to the classical and modern theory of polyanalytic functions and their generalizations. This is a subbranch of complex analysis of several…

This paper is a greatly expanded version of a talk I gave in April 2009 at KunenFest. It describes Ken's work in algebra, particularly using automated deduction tools.

Tate's theorem (Invent. Math. 1966)implies that the Tate conjecture holds for any abelian variety over a finite field whose Q_l-algebra of Tate classes is generated by those of degree 1. We construct families of abelian varieties over…

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.

This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.

In this paper we will prove that Tate conjecture of abelian varieties over finite field is equivalent to the finiteness of isomorphism classes of abelian varieties with a fixed dimension. We give a different approach with Zarhin's result.

In this paper, we define, for arithmetic schemes with semistable reduction, $p$-adic objects playing the roles of Tate twists in \'etale topology, and establish their fundamental properties.

The paper is a chapter of the above-mentioned book. It aims to give an expository presentation of author's version of the non-Abelian Stokes theorem in the framework of path-integral formalism.

This is my laudation for Scholze's Fields medal 2018.

We propose iteratively prompting a large language model to self-correct a translation, with inspiration from their strong language understanding and translation capability as well as a human-like translation approach. Interestingly,…

This note announces recent exciting progress on the frontier between algebraic topology and probability theory. It is intended for a journal which publishes such announcements (without an abstract, typically in Russian). A description of a…

I outline Bell's vision of the "great enterprise" of science, and his view that conventional teachings about quantum mechanics constituted a betrayal of this enterprise. I describe a proposal of his to put the theory on a more satisfactory…

This is the paper "Niels Henrik Abel and the birth of fractional calculus", Podlubny, I., Magin, R. L., Trymorush I., Fractional Calculus and Applied Analysis, vol.20, no.5, pp.1068-1075, 2017 (https://doi.org/10.1515/fca-2017-0057) with…