Related papers: The level 1 weight 2 case of Serre's conjecture

We reformulate a conjecture of Deligne on 1-motives by using the integral weight filtration of Gillet and Soul\'e on cohomology, and prove it. This implies the original conjecture up to isogeny. If the degree of cohomology is at most two,…

We give a proof of the Greene-Krantz conjecture on convex domains in $\CC^2$. Curiously, the proof technique depends on subelliptic estimates for the $\bar{\partial}$ problem.

We formulate several conjectures which shed light on the structure of Veronese syzygies of projective spaces. Our conjectures are based on experimental data that we derived by developing a numerical linear algebra and distributed…

We prove the Tate conjecture for divisor classes and the Mumford-Tate conjecture for the cohomology in degree 2 for varieties with $h^{2,0}=1$ over a finitely generated field of characteristic 0, under a mild assumption on their moduli. As…

We present a streamlined and simplified proof of the Kakeya set conjecture in $\mathbb{R}^3$.

We investigate the existence of the limit of some high order weighted Cesaro averages.

We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

This is a survey on Sarnak's Conjecture

We give some results on a priori estimates and on estimates of type sup+inf and sup*inf.

We construct two Frechet algebras admitting countably many mutually inequivalent Frechet algebra topologies. The second example is a modification of the maiden (and first) example of a non-Banach Frechet algebra with two inequivalent…

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.

We prove that two dimensional convex subsets of spherical buildings are either buildings or have a center.

We first prove the existence of minimally ramified p-adic lifts of 2-dimensional mod p representations, that are odd and irreducible, of the absolute Galois group of Q,in many cases. This is predicted by Serre's conjecture that such…

We construct a positive-dimensional, reducible Severi variety on a toric surface.

We present a nonstandard simple elementary proof of Szemer\'{e}di's theorem by a straightforward induction with the help of three levels of infinities and four different elementary embeddings in a nonstandard universe.

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.

We prove the conjecture that higher Verlinde categories are geometrically reductive. This is one of the two properties required in order for recent results on algebraic geometry in tensor categories to apply to these categories. We also…