Related papers: The Work of John Tate

This is a manuscript to be published as a book chapter. The text summarizes some of my critics concerning Everett's theory as seen from the perspective of a Bohmian. This is the second draft and comments are still welcome.

Generative Artificial Intelligence constitutes a new wave of automation. There is broad agreement among economists that humanity is potentially entering into a period of profound change. However, significant uncertainties and disagreements…

This paper is an investigation into Cantor works about representing a function with trigonometric series, and his proofs about its uniqueness. These works are important, because they cause invention of point-set topology, and foundation of…

This survey describe Hodge, Tate and Mumford-Tate conjectures for abelian varieties. After some preliminaries on endomorphism ring, polarization and algebraic cycles, we state the three conjectures and provide a list of know results.…

The main subjects of this text are: (1) Generalization of concepts and operations, like distance and size, to situations where they are not definable in the usual way. (2) A pragmatic theory of handling contradictions using reliability of…

My paper "Talking About Large Language Models" has more than once been interpreted as advocating a reductionist stance towards large language models. But the paper was not intended that way, and I do not endorse such positions. This short…

Success in academia hinges on publishing in top tier journals. This requires innovative results. And this requires clear and convincing presentation of said results. Presentation can make the difference of one tier in journal level. A lot…

This is an English translation of Felix Klein's paper "Ueber die Transformation elfter Ordnung der elliptischen Functionen" from 1879.

This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…

We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika…

These notes are devoted to the theory of exponential sums over finite fields. The first chapter recalls some of the number-theoretic interest of such sums. The second chapter discusses the $L$-functions attached to such sums, the "Weil…

The paradigm of Big Data has been established as a solid field of studies in many areas such as healthcare, science, transport, education, government services, among others. Despite widely discussed, there is no agreed definition about the…

This article is a conceptual exposition on the structure of the tree. It demonstrates an evolutionary design that the tree possesses in the perspective of a structural engineer.

This is the second of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. One of the many…

Each researcher should have a full shelf---physical or virtual---of books on writing and editing prose. Though we make no claim to any special degree of expertise, we recently edited a book of complexity theory surveys (Complexity Theory…

The Tate conjecture has two parts: an assertion (S) about semisimplicity of Galois representations, and an assertion (T) which says that every Tate class is algebraic. We show that in characteristic 0, (T) implies (S). In characteristic p…

We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.

This note concerns exponential sheaves and the "universal" Fourier transform on them. Fourier invertibility and the subsequent Fourier miracle is demonstrated. Further, t-structures and realizations are constructed and shown to have…

I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James…

This is the first of several monographs to be devoted to the optics of accelerated systems. They are being published for the benefit of those who may wish to have another way of looking at kineoptical problems, and also to demonstrate that…