Hilbert Functions and the Koszul Complex

1970 ◽  
Vol 2 (1) ◽  
pp. 69-72 ◽  
Author(s):  
D. G. Northcott
Keyword(s):  
Koszul Complex ◽  
Hilbert Functions

Hilbert Functions and the Koszul Complex

1981 ◽  
Vol s2-24 (3) ◽  
pp. 459-466 ◽  
Author(s):  
David Kirby ◽  
Hefzi A. Mehran
Keyword(s):  
Koszul Complex ◽  
Hilbert Functions

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

Hilbert functions and the extension functor

1989 ◽  
Vol 105 (3) ◽  
pp. 441-446 ◽  
Author(s):  
David Kirby
Keyword(s):  
Commutative Ring ◽  
Hilbert Functions ◽  
Definition Of

Throughout R will denote a commutative ring with identity, A,B etc. will denote ideals of R, and E will denote a unitary R-module. We recall from [5] the definition of homological grade hgrR(A;E) as inf{r|ExtRr(R/A,E) ≠ 0}, and we allow both hgrR(A;E) = ∞ (i.e. ExtRr(R/A,E) = 0 for all r) and AE = E. For the most part E will be Noetherian, in which case hgrR(A;E) coincides with the usual grade grR(A;E) which is the supremum of the lengths of the (weak) E-sequences contained in A (see [7], for example).

scholarly journals Interval conjectures for level Hilbert functions

2009 ◽  
Vol 321 (10) ◽  
pp. 2705-2715 ◽  
Author(s):  
Fabrizio Zanello
Keyword(s):  
Hilbert Functions

Gröbner bases specialization through Hilbert functions

2000 ◽  
Vol 34 (1) ◽  
pp. 1-8 ◽  
Author(s):  
M.-J. Gonzalez-Lopez ◽  
L. Gonzalez-Vega ◽  
C. Traverso ◽  
A. Zanoni
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Hilbert Functions
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