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Some results on the cofiniteness of local cohomology modules

Sohrab Sohrabi Laleh, Mir Yousef Sadeghi, Mahdi Hanifi Mostaghim (2012)

Czechoslovak Mathematical Journal

Let R be a commutative Noetherian ring, 𝔞 an ideal of R , M an R -module and t a non-negative integer. In this paper we show that the class of minimax modules includes the class of 𝒜ℱ modules. The main result is that if the R -module Ext R t ( R / 𝔞 , M ) is finite (finitely generated), H 𝔞 i ( M ) is 𝔞 -cofinite for all i < t and H 𝔞 t ( M ) is minimax then H 𝔞 t ( M ) is 𝔞 -cofinite. As a consequence we show that if M and N are finite R -modules and H 𝔞 i ( N ) is minimax for all i < t then the set of associated prime ideals of the generalized local cohomology module...

Some surfaces with maximal Picard number

Arnaud Beauville (2014)

Journal de l’École polytechnique — Mathématiques

For a smooth complex projective variety, the rank ρ of the Néron-Severi group is bounded by the Hodge number h 1 , 1 . Varieties with ρ = h 1 , 1 have interesting properties, but are rather sparse, particularly in dimension 2 . We discuss in this note a number of examples, in particular those constructed from curves with special Jacobians.

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