We prove new modularity lifting theorems for p-adic Galois representations in situations
where the methods of Wiles and Taylor–Wiles do not apply. Previous generalizations of …

Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are
becoming increasingly important also in Computational Algebra. They capture many useful …

We prove new modularity lifting theorems for p-adic Galois representations in situations
where the methods of Wiles and Taylor--Wiles do not apply. Previous generalizations of …

In this paper we solve a problem posed by ME Rossi: Is the Hilbert function of a Gorenstein
local ring of dimension one not decreasing? More precisely, for any integer h> 1, h∉{14+ 22 …

In this paper we give necessary and sufficient conditions for the Cohen-Macaulayness of the
tangent cone of a monomial curve in 4-dimensional affine space. We particularly study the …

We study the minimal free resolution of the tangent cone of Gorenstein monomial curves in
affine 4-space. We give the explicit minimal free resolution of the tangent cone of …

We collect some open problems about minimal presentations of numerical semigroups and,
more generally, about defining ideals and free resolutions of their semigroup rings and …

We study monomial curves, toric ideals and monomial algebras associated to 4-generated
pseudo symmetric numerical semigroups. Namely, we determine indispensable binomials of …

In this article we solve the following problem:“The Hilbert function of the local ring of a 4-
generated pseudo-symmetric numerical semigroup is always non-decreasing.” We give a …

Given a one-dimensional semigroup ring R= k [[S]], in this article we study the behaviour of
the Hilbert function H R. By means of the notion of support of the elements in S, for some …