Algebraic loops and Drinfeld modules

• Grant number: 13/10596-8
• Support type: Research Grants - Visiting Researcher Grant - International
• Duration: August 10, 2013 - August 13, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Alexandre Grichkov
• Grantee: Alexandre Grichkov
• Visiting researcher: Dmitrii Logachev
• Visiting researcher institution: Universidad Simón Bolívar (USB), Venezuela
• Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 10/50347-9 - Algebras, representations e applications, AP.TEM

Abstract

We will study the Drinfeld modules and their generalizations. For this we interpretate an action of Hecke operators in term of action some algebraic group on affine Grassman variety. We begin the systematic study of algebraic Moufang and diassociative loops. In particulary, we will study of structure of diassociative local loop on cubic superface (Yu.Manins Problem). (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GRISHKOV, A.; LOGACHEV, D. Lattice map for Anderson t-motives: First approach. JOURNAL OF NUMBER THEORY, v. 180, p. 373-402, NOV 2017. Web of Science Citations: 0.

GRISHKOV, A.; LOGACHEV, D. Resultantal varieties related to zeroes of L-functions of Carlitz modules. FINITE FIELDS AND THEIR APPLICATIONS, v. 38, p. 116-176, MAR 2016. Web of Science Citations: 1.