Related papers: Brauer's Height Zero Conjecture for Principal Bloc…

Bishnoi conjectured that if a minimal t-fold blocking set in a projective plane of prime power order has maximal size then it is either a projective plane minus one point, the complement of a Baer subplane or a unital. In this note we prove…

Using geometric methods we prove the standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a finite field.

We prove the conjecture stated by Spencer Bloch in 1975 and saying that the Albanese kernel of a smooth projective surface is 0, provided its second cohomology group is algebraic.

We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.

The Segre-Gimigliano-Harbourne-Hirschowitz Conjecture can be naturally formulated for Hirzebruch surfaces F_n. We show that this Conjecture holds for imposed base points of equal multiplicity bounded by 8.

In the representation theory of finite groups, there is a well-known and important conjecture, due to Brou\'e saying that for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding…

A conjecture for higher order separation on generic rational surfaces with some new results about standard divisors.

We prove that the index of a Brauer class satisfies prime decomposition over a general base scheme. This contrasts with our previous result that there is no general prime decomposition of Azumaya algebras.

Motivated by various equivalent versions of the SHGH conjecture for $\mathbb{P}^2$ blown up at very general points, we propose a similar conjecture for Hirzebruch surfaces. We prove that this conjecture is true for the Hirzebruch surface…

In this short note, we state a stable and a $\tau$-reduced version of the second Brauer-Thrall Conjecture. The former is a slight strengthening of a brick version of the second Brauer-Thrall Conjecture raised by Mousavand and…

The Brauer monoid is studied by the notion of 0-cohomology. We investigate the impact of invertible elements of modifications on the structure of the Brauer monoid, especially for finite fields.

Using recent developments in the theory of mixed motives, we prove that the log Bloch conjecture holds for an open smooth complex surface if the Bloch conjecture holds for its compactification. This verifies the log Bloch conjecture for all…

We study the representation theory of the cyclotomic Brauer algebra via truncation to idempotent subalgebras which are isomorphic to a product of walled and classical Brauer algebras. In particular, we determine the block structure and…

We formulate an Iwasawa main conjecture for a higher rank Euler system for a general motive. We prove "one half" of the main conjecture under mild hypotheses. We also formulate a conjecture on "Darmon-type derivatives" of Euler systems and…

In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this paper we discuss further these conjectures and put forward…

In this paper, we prove a conjecture proposed by George Beck, which involves gap-free partitions and partitions with distinct parts.

We give a counter example to a conjecture of E. Bueler stating the equality between the DeRham cohomology of complete Riemannian manifold and a weighted $L^2$ cohomology where the weight is the heat kernel.

We study the failure of the integral Hasse principle and strong approximation for the Erd\H{o}s-Straus conjecture using the Brauer-Manin obstruction.

Let $(\mathcal{A},\Theta)$ be a length category. We introduce the notation of Gabriel-Roiter measure with respect to $\Theta$ and extend Gabriel's main property to this setting. Using this measure, when $(\mathcal{A},\Theta)$ satisfies some…

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.