Related papers: Equivalent version of Huppert's conjecture for $K_…
We state the analogs of Kontsevich's formality conjecture for Hochschild and cyclic chains, as well as their
In this note, we prove the K- and L-theoretic Farrell-Jones Conjecture with coefficients in an additive category for fundamental groups of graphs of virtually cyclic groups.
In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.
Recently, Nekrasov discovered a new "genus" for Hilbert schemes of points on $\mathbb{C}^4$. We conjecture a DT/PT correspondence for Nekrasov genera for toric Calabi-Yau 4-folds. We verify our conjecture in several cases using a vertex…
We present some new results on the cohomology of a large scope of SL\_2-groups in degrees above the virtual cohomological dimension; yielding some partial positive results for the Quillen conjecture in rank one. We combine these results…
Let $G$ be a nontrivial finite subgroup of $\SL_n(\C)$. Suppose that the quotient singularity $\C^n/G$ has a crepant resolution $\pi\colon X\to \C^n/G$ (i.e. $K_X = \shfO_X$). There is a slightly imprecise conjecture, called the McKay…
The Tate conjecture for divisors on varieties over number fields is equivalent to finiteness of $\ell$-primary torsion in the Brauer group. We show that this finiteness is actually uniform in one-dimensional families for varieties that…
We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.
We prove the equality of three conjectural formulas for the Brumer--Stark units. The first formula has essentially been proven, so the present paper also verifies the validity of the other two formulas.
This short note shows how the Novikov conjecture for mapping class groups follows from a theorem of Kato and a result theorem of Hamenstadt.
We show that for various natural classes of groups and appropriately defined K- and L-theoretic functors, injectivity or bijectivity of the assembly map follows from the Isomorphism Conjecture being true for acyclic groups lying within that…
The present article gives the index formula of the principal congruence subgroups of the Hecke group H_5
In this paper we consider the remaining cases of Hebey-Vaugon conjecture.
This note surveys axiomatic results for the Farrell-Jones Conjecture in terms of actions on Euclidean retracts and applications of these to GL_n(Z), relative hyperbolic groups and mapping class groups.
We present the status of the Farrell-Jones Conjecture for algebraic K-theory for a group G and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be true and study inheritance properties. We discuss new…
We construct uncountably categorical 3-nilpotent groups of exponent p > 3. They are not one-based and do not allow the interpretation of an infinite field. Therefore they are counterexamples to Zilbers Conjecture. First 2-nilpotent new…
We show that Hardy's uncertainty principle can be reformulated in such a way that it has an analogue even for compact Lie groups and symmetric spaces of compact type.
We show, using basic Morita equivalences between block algebras of finite groups, that the Conjecture of H. Sasaki from [9] is true for a new class of blocks called nilpotent covered blocks. When this Conjecture is true we define some…
We reveal a correspondence between the homological torsion of the Bianchi groups and new geometric invariants, which are effectively computable thanks to their action on hyperbolic space. We use it to explicitly compute their integral group…
We study the Hodge conjecture for powers of K3 surfaces and show that if the Kuga--Satake correspondence is algebraic for a family of K3 surfaces of generic Picard number 16, then the Hodge conjecture holds for all powers of any K3 surface…