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We identify Le Potier's moduli spaces of limit stable pairs $(F,s)$, where$F$ is a 2-dimensional sheaf on a nonsingular projective 4-fold $X$ and $s \inH^0(F)$, with the moduli spaces of polynomial stable 2-term complexes inderived category. These stable pairs are 2-dimensional analogs ofPandharipande-Thomas' stable pairs defined for 3-folds. We establishcategorical correspondences involving these stable pairs, ideal sheaves of2-dimensional subschemes of $X$, and 1-dimensional sheaves on $X$. Under someconditions on the Chern character, these lead to Hall algebra correspondences.The generalization of most of these results to higher ranks is also given.  In case $X$ is Calabi-Yau, Oh-Thomas' construction gives a new set ofinvariants of $X$ counting these stable pairs. For certain Chern characters,these are related to the invariants of 2-dimensional stable sheaves. Wecalculate and study them in some cases and examples such as fibrations byabelian surfaces, local surfaces, and local Fano 3-folds. The last case inparticular leads to new invariants of Fano 3-folds counting 2-dimensionalstable pairs with reduced supports.

Stable pairs of 2-dimensional sheaves on 4-folds