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LAURENT COEFFICIENTS AND EXT OF FINITE GRADED MODULES
 

Summary: LAURENT COEFFICIENTS AND EXT
OF FINITE GRADED MODULES
Luchezar L. Avramov
Ragnar-Olaf Buchweitz
Judith D. Sally
Abstract. Let M and N be nite graded modules over a graded commutative ring generated
over a eld K = R0 by homogeneous elements x1 ; : : : ; xe of positive degrees d1 ; : : : ; de . By
the Hilbert-Serre Theorem, the Hilbert series
P
n2Z (rank K Mn )t n is the Laurent expansion
around t = 0 of a rational function HM (t) = q M (t)=
Q e
i=1 (1 t d i ) with q M (t) 2 Z[t;t 1 ].
The main result in this paper establishes an equality of rational functions
X
i
( 1) i H Ext i
R (M;N) (t) = HM (t 1 )  HN (t)
HR (t 1 )
when Ext i

  

Source: Avramov, Luchezar L.- Department of Mathematics, University of Nebraska-Lincoln

 

Collections: Mathematics