HPD-inv of TBR · (Homological Projective Duality)-invariance of the Tate, Beilinson and Riemann conjectures
„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“
- Период
- 2020-09-01 → 2022-08-31
- Финансиране от ЕС
- 224 934 €
- Участници
- 1
- Схема
- MSCA-IF
Линиите свързват координатора с партньорите.
Накратко на български
Математическите хипотези на Тейт, Бейлинсън и Риман изследват разположението на нулите и полюсите на L-функциите. Доказването, че те са инвариантни при хомологична проективна дуалност, помага за разбирането на някои от най-трудните проблеми в математиката.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
(Homological Projective Duality)-invariance of the Tate, Beilinson and Riemann conjectures
Three of the most important conjectures in mathematics - the Tate conjecture, the Beilinson conjecture and the generalized Riemann hypothesis - concern the location and order of the zeros/poles of the L-functions. These conjectures play a central role in mathematics. For example, in the particular case of an elliptic curve, the Beilinson conjecture reduces to the Birch and Swinnerton-Dyer conjecture, and in the particular case of a point, the generalized Riemann hypothesis reduces to the famous Riemann hypothesis. These are two of the seven Millennium Prize Problems. The overall objective of this project is to prove that the aforementioned conjectures of Tate, Beilinson, and Riemann, are invariant under homological projective duality.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
This project will be carried out at the Warwick Mathematics Institute under the supervision of Prof. John Greenlees; I have worked for the past eight years at MIT and I will move in 2020 to the University of Warwick as an Associate Professor. Three of the most important conjectures in mathematics - the Tate conjecture, the Beilinson conjecture and the generalized Riemann hypothesis - concern the location and order of the zeros/poles of the L-functions associated to algebraic varieties. For example, in the particular case of an elliptic curve, the Beilinson conjecture reduces to the Birch and Swinnerton-Dyer conjecture, and in the particular case of a point, the generalized Riemann hypothesis reduces to the Riemann hypothesis. These are two of the seven Millenium Prize Problems. The first objective of this project is to prove that the conjectures of Tate, Beilinson, and Riemann, are invariant under homological projective duality in the sense of Kuznetsov. The second objective is to combine this invariance result with the different homological projective dualities in the literature in order to obtain not only a proof of the conjectures of Tate and Beilinson in numerous new cases but also an equivalence between the generalized Riemann hypothesis of very different algebraic varieties. These objectives will greatly improve the state-of-the-art of the Tate and Beilinson conjectures and will considerably deepen our understanding of the generalized Riemann hypothesis. In order to achieve them, I will combine Kontsevich's noncommutative viewpoint on algebraic geometry with mathematical tools from several different areas (e.g., algebraic topology, derived categories, algebraic K-theory, etc). This will enhance my creative and innovative potential, will foster my professional maturity and independence, will diversify my technical skills, and also will enable me to receive advanced training. Hence, this project is directly aligned with the MSCA-IF-EF-RI objectives.
Оригинален текст от CORDIS (на английски).
Участници
- UNIVERSITY OF WARWICK · COVENTRYКоординаторОбединеното кралство
Връзки
Данни: CORDIS, © Европейски съюз