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pro vyhledávání: '"Logachev, Dmitry"'
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 Carlitz modules. It contains a conjecture that some of these varieties
Externí odkaz:
http://arxiv.org/abs/2209.04044
Autor:
Grishkov, Aleksandr, Logachev, Dmitry
We formulate some properties of a conjectural object $X_{fun}(r,n)$ parametrizing Anderson t-motives of dimension $n$ and rank $r$. Namely, we give formulas for $\goth p$-Hecke correspondences of $X_{fun}(r,n)$ and its reductions at $\goth p$ (where
Externí odkaz:
http://arxiv.org/abs/2102.03922
We consider Anderson t-motives $M$ of dimension 2 and rank 4 defined by some simple explicit equations parameterized by $2\times2$ matrices. We use methods of explicit calculation of $h^1(M)$ -- the dimension of their cohomology group $H^1(M)$ ( = th
Externí odkaz:
http://arxiv.org/abs/2006.00316
Autor:
Grishkov, Aleksandr, Logachev, Dmitry
Let $M$ be an Anderson t-motive of dimension $n$ and rank $r$. Associated are two $\Bbb F_q[T]$-modules $H^1(M)$, $H_1(M)$ of dimensions $h^1(M)$, $h_1(M)\le r$ - analogs of $H^1(A,\Bbb Z)$, $H_1(A,\Bbb Z)$ for an abelian variety $A$. There is a theo
Externí odkaz:
http://arxiv.org/abs/1807.08675
We prove two polynomial identities which are particular cases of a conjecture arising in the theory of L-functions of twisted Carlitz modules. This conjecture is stated in earlier papers of the second author.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/1707.04339
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 of Carlitz modules". These varieties are related with the Sylvester ma
Externí odkaz:
http://arxiv.org/abs/1607.06147
Autor:
Logachev, Dmitry
Publikováno v:
Constructive algebraic geometry, 1981, N.194, p. 79 -- 82 (Russian)
We consider a locally free sheaf $F$ of dimension 2 on $P^2$. A conic $q$ on $P^2$ is called a jumping conic if the restriction of $F$ to $q$ is not the generic one. We prove that the set of jumping conics is the maximal determinantal variety of a sk
Externí odkaz:
http://arxiv.org/abs/1301.1866
We show that there exists a connection between two types of objects: some kind of resultantal varieties over C, from one side, and varieties of twists of the tensor powers of the Carlitz module such that the order of 0 of its L-functions at infinity
Externí odkaz:
http://arxiv.org/abs/1205.2900
Autor:
Grishkov, Aleksandr, Logachev, Dmitry
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 local result that sheds the first light to this problem and suggests tha
Externí odkaz:
http://arxiv.org/abs/1109.0679
Autor:
Logachev, Dmitry
Kolyvagin proved that the Tate-Shafarevich group of an elliptic curve over Q of analytic rank 0 or 1 is finite, and that its algebraic rank is equal to its analytic rank. A program of generalisation of this result to the case of some motives which ar
Externí odkaz:
http://arxiv.org/abs/math/0411346