Related papers: Hebey-Vaugon conjecture II
In this paper, we generalize some conclusions from the nonnegative irreducible tensor to the nonnegative weakly irreducible tensor and give more properties of eigenvalue problems.
We consider some bases in the Hecke algebra and exhibit certain dualities between them.
These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
In this paper we state some conjectures about q-Fibonacci polynomials which for q=1 reduce to well-known results about Fibonacci numbers and Fibonacci polynomials.
We define and compare two bivariant generalizations of the topological $K$-group $K^\top(G)$ for a topological group $G$. We consider the Baum-Connes conjecture in this context and study its relation to the usual Baum-Connes conjecture.
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
In this paper, we propose the study of a conjecture whose affirmative solution would provide an example of a non-convex Chebyshev set in an infinite-dimensional real Hilbert space.
We refine the conditions for the lower bound in an abstract large deviation result with nonconvex rate function we had previously introduced. We apply the results to certain stochastic recursive schemes.
The Hodge Conjecture is equivalent to a statement about conditions under which a complex vector bundle on a smooth complex projective variety admits a holomorphic structure. I advertise a class of abelian four-folds due to Mumford where…
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
This survey describe Hodge, Tate and Mumford-Tate conjectures for abelian varieties. After some preliminaries on endomorphism ring, polarization and algebraic cycles, we state the three conjectures and provide a list of know results.…
Six conjectures on pairs of consecutive primes are listed in this paper, together with examples for each case.
This is an expository paper based on the results in [12] and [16]. The main goal is to prove the following two conjectures for genus up to two. (1) Witten's conjecture on the relations between higher spin curves and Gelfand-Dickey…
We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…
We survey three results on syzygies of curves beyond Green's conjecture, with a particular emphasis on drawing connections between the study of syzygies and other topics in moduli theory.