ﻻ يوجد ملخص باللغة العربية
We prove that if the Jacobian Conjecture in two variables is false and (P,Q) is a standard minimal pair, then the Newton polygon HH(P) of P must satisfy several restrictions that had not been found previously. This allows us to discard some of the corners found in [GGV, Remark 7.14] for HH(P), together with some of the infinite families found in [H, Theorem~2.25]
This article has been withdrown by the author.
Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with $T^times = k^times$. Then T = S.
We describe an algorithm that computes possible corners of hypothetical counterexamples to the Jacobian Conjecture up to a given bound. Using this algorithm we compute the possible families corresponding to $gcd(deg(P),deg(Q))le 35$, and all the pair
Let $K$ be any field and $x = (x_1,x_2,ldots,x_n)$. We classify all matrices $M in {rm Mat}_{m,n}(K[x])$ whose entries are polynomials of degree at most 1, for which ${rm rk} M le 2$. As a special case, we describe all such matrices $M$, which are th
In this short review we first recall combinatorial or ($0-$dimensional) quantum field theory (QFT). We then give the main idea of a standard QFT method, called the intermediate field method, and we review how to apply this method to a combinatorial Q