Exponential Growth of Betti Numbers
نویسنده
چکیده
We prove over some local commutative noetherian rings that the sequence of Betti numbers of every finitely generated module is either eventually constant or has termwise exponential growth.
منابع مشابه
TORSION NUMBERS OF AUGMENTED GROUPS with applications to knots and links
ABSTRACT. Torsion and Betti numbers for knots are special cases of more general invariants br and βr, respectively, associated to a finitely generated group G and epimorphism χ : G → Z. The sequence of Betti numbers is always periodic; under mild hypotheses about (G,χ), the sequence br satisfies a linear homogeneous recurrence relation with constant coefficients. Generally, br exhibits exponent...
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