Algebraic loops and Drinfeld modules

• Grant number: 13/10596-8
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 10, 2013
• End date: 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
• Host 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.. Resultantal varieties related to zeroes of L-functions of Carlitz modules. FINITE FIELDS AND THEIR APPLICATIONS, v. 38, p. 116-176, MAR 2016. (13/10596-8)

GRISHKOV, A.; LOGACHEV, D.. Lattice map for Anderson t-motives: First approach. JOURNAL OF NUMBER THEORY, v. 180, p. 373-402, NOV 2017. (13/10596-8)