Related papers: A Counter Example To the Hodge Conjecture

Khabibullin's conjecture has three statements equivalent to each other. Recently Ruslan Sharipov has constructed a counterexample to this conjecture for one of its three statements. In this paper Sharipov's counterexample is transferred to…

We establish a simple generalization for the famous theorem of Morley about trisectors in triangle with a purely synthetic proof using only angle chasing and similar triangles. Furthermore, based on the converse construction, another simple…

We upgrade Howard's divisibility toward Perrin-Riou's Heegner point Main Conjecture to an equality under some mild conditions. We do this by exploiting Wei Zhang's proof of the Kolyvagin conjecture. The main ingredient is an improvement of…

A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.

We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general fibers smooth complete intersections, we prove the conjecture…

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…

Let A be an abelian fourfold. We prove the Standard Conjecture of Hodge type for A. By combining this result with a theorem of Clozel we deduce that numerical equivalence on A coincides with l-adic homological equivalence on A for…

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.

We give a proof of the Howe duality conjecture for the (almost) equal rank dual pairs in full generality. For arbitrary dual pairs, we prove the irreducibility of the (small) theta lifts for all tempered representations. Our proof works for…

We present a conjecture about partitions, with a very elementary formulation.

We give a one-sentence proof of McLaughlin and Rundell's inverse uniqueness theorem.

In [2] the author claims to provide a counterexample to a result in a recent paper [1]. In this note, we prove that the details of his example is false and this example is compatible with our result in [1] and so is not a countreexample.

In this paper we prove the WALA conjecture.

An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.

We prove in this paper the Ax-Schanuel conjecture for all admissible variations of mixed Hodge structures.

We give a detailed exposition of the homotopy theory of equivalence relations, perhaps the simplest nontrivial example of a model structure.

We give a minimal counterexample for a conjecture of Ross and Yong (2015) which proposes a K-Kohnert rule for Grothendieck polynomials. We conjecture a revised version of this rule. We then prove both rules hold in the $321$-avoiding case.

Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…

We prove some extensions of Andrews inequality.

In this note we provide some counterexamples for the conjectures of finite simple groups, one of the conjectures said "all finite simple groups $G$ can be determined using their orders $|G|$ and the number of elements of order $p$, where…