相关论文: Notes on the Milnor conjectures

General considerations on the Equivalence conjectures and a review of few mathematical results.

The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

An introduction to circle valued Morse theory and Novikov homology, from an algebraic point of view.

The Virasoro conjecture is a conjectured sequence of relations among the descendent Gromov-Witten invariants of a smooth projective variety in all genera; the only varieties for which it is known to hold are a point (Kontsevich) and…

We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.

We discuss cases where Voevodsky's smash nilpotence conjecture is known, and give a few new ones. In particular we explain a theorem of the cube for $1$-cycles, which is due to Oussama Ouriachi.

We give a concise exposition of Voevodsky's theory of motives.

Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

In this note we generalize and prove a recent conjecture of Varchenko concerning the number of critical points of a (multivalued) meromorphic function $\phi$ on an algebraic manifold. Under certain conditions, this number turns out to…

An observation on Hall-Littlewood polynomials.

According to some discussions based on syllogism, we present results on the binary Goldbach conjecture in three categories: results that are weaker than the Goldbach conjecture, sufficient conditions for the Goldbach conjecture, and results…

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

In a paper of Kedlaya and Medvedovsky, the number of distinct dihedral mod 2 modular representations of level N was calculated, and a conjecture on the dimension of the space of level N weight 2 modular forms giving rise to each…

We show how the techniques of Voevodsky's proof of the Milnor conjecture and the Voevodsky- Rost proof of its generalization the Bloch-Kato conjecture can be used to study counterexamples to the classical L\"uroth problem. By generalizing a…

In the article [PR1] {\it On Hrushovski's proof of the Manin-Mumford conjecture} (Proceedings of the ICM 2002), R. Pink and the author gave a short proof of the Manin-Mumford conjecture, which was inspired by an earlier model-theoretic…

Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.

We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type…

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings, respectively, in the context of (locally) essential domains.