Anderson t-motives, their L-functions and lattices

• Grant number: 17/19777-6
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil
• Start date: January 01, 2018
• End date: December 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Alexandre Grichkov
• Grantee: Alexandre Grichkov
• Visiting researcher: Dmitry Logachev
• Visiting researcher institution: Universidade Federal do Amazonas (UFAM). Instituto de Ciências Exatas, Brazil
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 14/09310-5 - Algebraic structures and their representations, AP.TEM

Abstract

Let M be an Anderson t-motive of dimension N and rank R. We can associate it a lattice L(M) in the space C(p), some analog of complex numbers in characteristic p. We will investigate the image of this map: M--L(M) and corresponding zeta-function Z(M)(t). (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.. h(1) not equal h(1) for Anderson t-motives. JOURNAL OF NUMBER THEORY, v. 225, p. 59-89, AUG 2021. (17/19777-6)

GRISHKOV, A.; LOGACHEV, D.; ZOBNIN, A.. L-functions of Carlitz modules, resultantal varieties and rooted binary trees - I. JOURNAL OF NUMBER THEORY, v. 238, p. 44-pg., 2022-05-26. (17/19777-6)

GRISHKOV, A.; LOGACHEV, D.. Anderson t-motives and abelian varieties with MIQF: Results coming from an analogy. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 21, n. 09, p. 12-pg., 2022-09-01. (17/19777-6)