Related papers: Mordell-Lang in positive characteristic
We ask questions generalizing uniform versions of conjectures of Mordell and Lang and combining them with the Morton--Silverman conjecture on preperiodic points. We prove a few results relating different versions of such questions.
We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.
In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…
We prove a version of the Manin-Mumford conjecture for semiabelian varieties over fields of positive characteristic. The proof presented here contains the details of the proof sketched by the author in the article "Diophantine geometry from…
Let G be a cocompact lattice in a virtually connected Lie group or the fundamental group of a 3-manifold. We prove the K-theoretic Farrell-Jones Conjecture (up to dimension one) and the L-theoretic Farrell-Jones Conjecture for G, where we…
We give a short proof of the inner product conjecture for the symmetric Macdonald polynomials of type $A_{n-1}$. As a special case, the corresponding constant term conjecture is also proved.
We generalize the proof of the Farrell-Jones conjecture for CAT(0)-groups to a larger class of groups in particular also containing all hyperbolic groups. This way we give a unified proof for both classes of groups.
We outline a proof of the categorical geometric Langlands conjecture for GL(2), as formulated in reference [AG], modulo a number of more tractable statements that we call Quasi-Theorems.
We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…
We give a very short proof that a subgroup of a free group that is positively generated cannot be part of a counterexample to the Generalized Hanna Neumann Conjecture.
In this short note we give a characterization of ZM-groups that uses the functions defined and studied in [3,4]. This leads to a proof of Conjecture 6 in [4].
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
The theory of total positivity for reductive groups is here extended to the case of symmetric spaces.
We prove an accessibility result for finitely generated groups that combines Sela's acylindrical accessibility with Linell accessibility.
We note that Pillay's result on the stability of an algebraically closed field with a predicate for a group of Lang type implies that number uniformity follows formally from the finiteness results analogous to Faltings' Theorem.
We prove several generalisations of the ping-pong lemma for negatively curved groups.
We develop the theory of p-Lie algebras of finite Morley rank. In particular, we obtain a quite complete characterization in the soluble case
We show that the $\ell$-adic Tate conjecture for divisors on smooth proper varieties over finitely generated fields of positive characteristic follows from the $\ell$-adic Tate conjecture for divisors on smooth projective surfaces over…
We prove the Identity Theorem for pro-$p$-groups with a single defining relation giving a positive feedback to a question of Serre on the structure of relation modules. A construction of "conjurings" indicates finality of our result in a…
We study invariant theory of the general linear supergroup in positive characteristic. In particular, we determine when the symmetric group algebra acts faithfully on tensor superspace and demonstrate that the symmetric group does not…