A. Grishkov

activity

20112023

most cited

h^{1} \neq = h_{1}

for Anderson t-motives

3 citations · 7 across the 8 of their papers we have counts for

collaborators

9 papers

math.NT2023

$h^{1}$ , $h_{1}$ of Anderson t-motives, systems of affine equations and non-commutative determinants

A. Grishkov, D. Logachev

The authors defined in " $h^{1} \neq = h_{1}$ for Anderson t-motives" the notion of an affine equation associated to a t-motive $M$ . Here we define two systems of affine equations associate…

math.NT2022

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…

math.NT2021

Reductions of Hecke correspondences on Anderson modular objects

Aleksandr Grishkov, Dmitry Logachev

We formulate some properties of a conjectural object $X_{f u n} (r, n)$ parametrizing Anderson t-motives of dimension $n$ and rank $r$ . Namely, we give formulas for $\goth p$-Hecke cor…

math.NT2020★ 1 cited

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.NT2020

Calculation of $h^{1}$ of some Anderson t-motives

Stefan Ehbauer, Aleksandr Grishkov, Dmitry Logachev

We consider Anderson t-motives $M$ of dimension 2 and rank 4 defined by some simple explicit equations parameterized by $2 \times 2$ matrices. We use methods of explicit calculation…

math.NT2018★ 2 cited

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 $δ$ from the set of these bases to a flag vari…

math.NT2018★ 3 cited

$h^{1} \neq = h_{1}$ for Anderson t-motives

Aleksandr Grishkov, Dmitry Logachev

Let $M$ be an Anderson t-motive of dimension $n$ and rank $r$ . Associated are two $F_{q} [T]$ -modules $H^{1} (M)$ , $H_{1} (M)$ of dimensions $h^{1} (M)$ , $h_{1} (M) \leq r$ - analogs of $H^1(A…

math.AG2016

L-functions of Carlitz modules, resultantal varieties and rooted binary trees, II

Aleksandr Grishkov, Dmitry Logachev, Aleksey Zobnin

We continue study of some algebraic varieties (called resultantal varieties) started in a paper of A. Grishkov, D. Logachev "Resultantal varieties related to zeroes of L-functions…

math.AG2011★ 1 cited

Lattice map for Anderson T-motives: first approach

Aleksandr Grishkov, Dmitry Logachev

There exists a lattice map from the set of pure uniformizable Anderson t-motives to the set of lattices. It is not known what is the image and the fibers of this map. We prove a lo…

h1, h1​ of Anderson t-motives, systems of affine equations and non-commutative determinants

Explicit statement of a conjecture on resultantal varieties

Reductions of Hecke correspondences on Anderson modular objects

Introduction to Anderson t-motives: a survey

Calculation of h1 of some Anderson t-motives

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

h1=h1​ for Anderson t-motives

L-functions of Carlitz modules, resultantal varieties and rooted binary trees, II

Lattice map for Anderson T-motives: first approach

$h^{1}$ , $h_{1}$ of Anderson t-motives, systems of affine equations and non-commutative determinants

Calculation of $h^{1}$ of some Anderson t-motives

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

$h^{1} \neq = h_{1}$ for Anderson t-motives