相关论文: Ma\~n\'e's conjectures in codimension one

In this paper, we prove Smale's mean value conjecture by making use of quasiconformal deformations and holomorphic motions.

We prove that the Tate conjecture in codimension $1$ over a finitely generated field follows from the same conjecture for surfaces over its prime subfield. In positive characteristic, this is due to de Jong--Morrow over $\mathbf{F}_p$ and…

We propose a framework to prove Malle's conjecture for the compositum of two number fields based on proven results of Malle's conjecture and good uniformity estimates. Using this method we can prove Malle's conjecture for $S_n\times A$ over…

In this paper we prove some results on the sufficiency of codimension-one fibre conditions for a flat algebra with a retraction to be locally $\mathbb{A}^1$ or at least an $\mathbb{A}^1$-fibration.

Building on work of M. M\"uger and L. Tuset, we reduce the Mathieu conjecture, formulated by O. Mathieu in 1997, for $SU(N)$ to a simpler conjecture in purely abelian terms. We sketch a similar reduction for $SO(N)$. The proofs rely on…

For the OEIS sequence A214615, defined by $a(n) = M_{n}(1)$ where $M_{n}$ is the $n$-th Meixner polynomial satisfying $M_{n+1}(x) = x\,M_{n}(x) - n^{2}\,M_{n-1}(x)$, R.~J.~Mathar contributed on 6~March 2013 the conjectured order-2…

Let M_d(k) denote the space of dxd-matrices with coefficients in an algebraically closed field k. Let X be an orbit closure in the product [M_d(k)]^t equipped with the action of the general linear group GL_d(k) by simultaneous conjugation.…

For the OEIS sequence A025166, defined by $a(n) = -n!\,2^{n}\,L_{n}(1/2)$ where $L_{n}$ is the Laguerre polynomial of degree $n$, R.~J.~Mathar contributed in February 2013 the conjectured order-2 P-recursive recurrence \[ a(n) + (-4n+3)\,…

We prove a computable version of the Hall Harem Theorem where the matching realizes a unary function with controlled sizes of cycles. We apply it to non-amenable computable coarse spaces. As a result, we obtain a computable version of the…

We prove a variant of Manin's conjecture for Campana points on wonderful compactifications of semi-simple algebraic groups of adjoint type. We use this to provide evidence for a new conjecture on the leading constant in Manin's conjecture…

We prove a convex integration result for the Monge-Amp\`ere system, in case of dimension $d=2$ and arbitrary codimension $k\geq 1$. Our prior result stated flexibility up to the H\"older regularity $\mathcal{C}^{1,\frac{1}{1+ 4/k}}$,…

The Pappas-Rapoport coherence conjecture, proved by Zhu, states that the dimensions of spaces of sections of certain line bundles coincide. The two sides of the equality correspond to the line bundles on spherical Schubert varieties in the…

Several results about the union-closed sets conjecture are presented.

We define invariants $\operatorname{inv}_1,\dots,\operatorname{inv}_m$ of Galois extensions of number fields with a fixed Galois group. Then, we propose a heuristic in the spirit of Malle's conjecture which asymptotically predicts the…

In this paper we prove a conjecture by De Concini, Kac and Procesi \cite{CP} (Corollary \ref{conj}): The dimension of any $M\in U_q-\mood^\chi$ is divisible by $l^{codim_\mathcal{B}\mathcal{B}_\chi}$.

We present a conjecture for expressing the coefficients in the Cayley-Hamilton theorem for supermatrices in terms of supertraces. The conjecture is tested for several supermatrix dimensions and unique results are obtained. Generating…

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

We prove a convex integration result for the Monge-Ampere system in dimension $d=2$ and arbitrary codimension $k\geq 1$. We achieve flexibility up to the Holder regularity $\mathcal{C}^{1,\frac{1}{1+ 4/k}}$, improving hence the previous…

We give a new, elementary proof of the fact that metric 1-currents in the Euclidean space correspond to Federer-Fleming flat chains.

A conjecture of May states that there is an up-to-adjunction strictification of symmetric bimonoidal functors between bipermutative categories. The main result of this paper proves a weaker form of May's conjecture that starts with…