Related papers: The Tate Thomason Conjecture

We make explicit a construction of Serre giving a definition of an algebraic Sato-Tate group associated to an abelian variety over a number field, which is conjecturally linked to the distribution of normalized L-factors as in the usual…

In this paper, we give an affirmative answer to Yamada's Conjecture on free topological groups, which was posed in [K. Yamada, {\it Fr\'echet-Urysohn spaces in free topological groups}, Proc. Amer. Math. Soc., {\bf 130}(2002), 2461--2469.].

We prove that the Tate conjecture is invariant under Homological Projective Duality (=HPD). As an application, we prove the Tate conjecture in the new cases of linear sections of determinantal varieties, and also in the cases of complete…

In this paper, we clarify and build connections between various conjectures largely motivated by the works of Jean-Pierre Serre and John Tate. We closely study the Tate conjecture for algebraic cycles as well as their motivic…

We consider an Archimedean analogue of Tate's conjecture, and verify the conjecture in the examples of isospectral Riemann surfaces constructed by Vigneras and Sunada. We also enunciate a simple lemma in group theory which lies at the heart…

We prove new cases of the Tate conjecture for abelian varieties over finite fields, extending previous results of Dupuy--Kedlaya--Zureick-Brown, Lenstra--Zarhin, Tankeev, and Zarhin. Notably, our methods allow us to prove the Tate…

We prove the Tits-Weiss conjecture for Albert division algebras over fields of arbitrary characteristics in the affirmative. The conjecture predicts that every norm similarity of an Albert division algebra is a product of a scalar homothety…

The Addition Theorem for the algebraic entropy of group endomorphisms of torsion abelian groups was proved in [4]. Later, this result was extended to all abelian groups [3] and, recently, to all torsion finitely quasihamiltonian groups [7].…

There are several proofs of the Fundamental Theorem of Algebra, mainly using algebra, analysis and topology. In this article, we have shown that the Fundamental Theorem of Algebra can be proved using Nevanlinna's first fundamental theorem…

We show that it is consistent that the Borel Conjecture and the dual Borel Conjecture hold simultaneously.

We settle in the affirmative the Graham-Sloane conjecture.

Let $G$ be a finite group, and let $N(G)$ be the set of sizes of its conjugacy classes. We show that if a finite group $G$ has trivial center and $N(G)$ equals to $N(Alt_n)$ or $N(Sym_n)$ for $n\geq 23$, then $G$ has a composition factor…

We describe an explicit `higher rank' Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of general number fields. We then show that this theory leads to a concrete new strategy for proving…

Given a smooth, proper family of varieties in characteristic $p>0$, and a cycle $z$ on a fibre of the family, we formulate a Variational Tate Conjecture characterising, in terms of the crystalline cycle class of $z$, whether $z$ extends…

The Atiyah conjecture for a discrete group G states that the $L^2$-Betti numbers of a finite CW-complex with fundamental group G are integers if G is torsion-free and are rational with denominators determined by the finite subgroups of G in…

This paper develops some general results about actions of finite groups on (infinite) abelian groups in the finite Morley rank category. They are linked to a range of problems on groups of finite Morley rank discussed in [16]. Crucially,…

We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.

We study the Fibered Isomorphism Conjecture of Farrell and Jones in L-theory for groups acting on trees. In several cases we prove the conjecture. This includes wreath products of abelian groups and free metabelian groups. We also deduce…

In this short article, we prove that any automorphism of the R. Thompson's group $F$ has infinitely many twisted conjugacy classes. The result follows from the work of Matthew Brin, together with a standard facts on R. Thompson's group $F$,…

In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.