D. Logachev

collaborators

4 papers

math.NT2025

Analytic ranks of twists of Carlitz modules -- a survey of results

A. Grishkov, D. Logachev

We give in this paper a survey of results obtained in our earlier papers, and state explicitly some problems of further research, for example: are the analytic ranks bounded, or no…

math.NT2025

Introduction to Anderson t-motives: a survey

A. Grishkov, D. Logachev

This is a survey on Anderson t-motives -- high-dimensional generalizations of Drinfeld modules. They are the functional field analogs of abelian varieties with multiplication by an…

math.NT2025

Lattice of the dual of an Anderson $t$ -motive in terms of a map to a flag variety

A. Grishkov, D. Logachev

Let $M$ be an uniformizable Anderson $t$ -motive of rank $r$ , $L$ its lattice and $l_{*} := {l_{1}, \dots, l_{r}}$ its basis. We define a map $I^´$ from the set of these bases to a flag var…

math.NT2025

Explicit statement of a conjecture on resultantal varieties

Stefan Ehbauer, Aleksandr Grishkov, Dmitry Logachev

The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of…

Analytic ranks of twists of Carlitz modules -- a survey of results

Introduction to Anderson t-motives: a survey

Lattice of the dual of an Anderson t-motive in terms of a map to a flag variety

Explicit statement of a conjecture on resultantal varieties

Lattice of the dual of an Anderson $t$ -motive in terms of a map to a flag variety