ayudug

Even from the practical standpoint, whatever people do aims to achieve some results in the future. The future is uncertain. Future-oriented action (which includes all practically purposeful action) is necessarily based on a belief about what the future is supposed to be. Such beliefs cannot be justified by purely empirical reasoning or trial and error approach. Any purposeful action requires an act of faith in the basic rules governing the future state of affairs and possible consequences. In this sense, all human action is grounded in faith; so it is religious in its basic nature.

The present-day person's religion is usually not the formal denomination, not Judaism or Catholicism or Protestantism. Those, nowadays, are mostly superficial labels which almost nobody takes very seriously. The actual religion is the most fundamental motivator, the common basis of all decisions the person makes and of everything he does with his life.

Typing 470 + 355 pages of original research in two manuscripts about contraherent cosheaves (a concept invented in the first one of the two manuscripts) is not the kind of thing modern mathematicians do. You can explain my decision to dedicate years of my life to such research by career considerations, or by me aiming to achieve some social effects in the community of mathematicians, etc. Such kind of considerations did indeed appear in my thoughts, reflection, and conscious, verbalized decision-making, as the readers of my blog could confirm. But any belief in desirable career consequences of dedicating my time to such research must be based on very unusual concepts of what is desirable and what can be expected as consequences.

My most basic motivation is, of course, to serve God by doing mathematics. Those manuscripts and my effort invested in working on them, just as all the other research work of mine, constitute an offering on the altar of God. The visible difference between my research and that of almost every other mathematician discloses a difference in religious beliefs. The God whom I worship and I strive to serve is not one of the gods that the state and the society are worshiping nowadays, in any country whatsoever. I am not worshiping the gods that the state and society are worshiping, that's what makes my behavior and my approach to life and mathematics look so unusual.

Essentially, I am a religious dissident. In secular terms, this means an extreme nonconformist, which is who I have always been. Religious dissidents have been persecuted harshly throughout the human history, and perhaps will always be. That is the root cause of all the bullying and persecution I have experienced in my life (and I've experienced quite a lot of it).

Working on my mathematical research generally and on the two book-sized manuscripts about contraherent cosheaves in particular brought me a lot of joy and genuine happiness, though it was hard work, of course. I intend to continue working on the subject and hopefully type another book-sized manuscript on another aspect of the theory. Of course, there are all kinds of practical and career-related considerations entering into my decision-making, which was usually the case in the recent decades. But the bottom line of all my thinking about the future that awaits me personally as the result of my efforts remains the same: as befits a religious dissident, I expect to be burned at the stake for my beliefs and contributions.

Двенадцатая версия -- https://arxiv.org/abs/2504.18460 . Эта версия уже мыслится как в основном полная (дальнейших масштабных добавлений не планируется). Больше 350 страниц, однако.

Эта версия обнародовалась еще вчера (во вторник) утром, но я был в отъезде и не пользовался интернетом, поэтому этот постинг публикуется здесь только сегодня под вечер.

Третий квартал 2025 года прошел. Больше 500 страниц в новых архивных препринтах написано и обнародовано за полгода с конца марта по конец сентября.

Допустим, еще в 2012-13 годах была у меня голубая мечта -- рассмотреть контрапроизводную категорию контрагерентных DG-контрамодулей над комплексом де Рама-Витта. Я даже вставил упоминание этой мечты во введение к препринту про контрагерентные копучки.

Что такое комплекс де Рама-Витта, я до сих пор не выучил, и даже толком не пытался. Не знаю, получится ли, когда-если попытаюсь. Но я давно знаю, что есть такой комплекс де Рама-Витта. Идея в том, что он, видимо, важен для алгебраической теории чисел и арифметической геометрии.

Зато я последовательно рассматривал:

- контрапроизводную категорию CDG-контрамодулей над CDG-коалгеброй над полем;
- производную и контрапроизводную категорию контрагерентных копучков над схемой;
- производную категорию контрамодулей над адическим пополнением коммутативного кольца;
- контрапроизводную категорию CDG-модулей над CDG-кольцом;
- контрапроизводную категорию контрамодулей над топологическим кольцом;
- контрапроизводную категорию контрагерентных DG-модулей над комплексом де Рама.

Чего недостает в этом списке частичных комбинаций основных ингредиентов? Кроме комплекса де Рама-Витта?

Конечно, недостает контрагерентных копучков контрамодулей! Контрагерентные копучки контрамодулей я пока еще не рассматривал. Но собираюсь.