Contraherent cosheaves
Abstract
Contraherent cosheaves are globalizations of cotorsion (or similar) modules over commutative rings obtained by gluing together over a scheme. The category of contraherent cosheaves over a scheme is a Quillen exact category with exact functors of infinite product. Over a quasicompact semiseparated scheme or a Noetherian scheme of finite Krull dimension (in a different version  over any locally Noetherian scheme), it also has enough projectives. We construct the derived cocontra correspondence, meaning an equivalence between appropriate derived categories of quasicoherent sheaves and contraherent cosheaves, over a quasicompact semiseparated scheme and, in a different form, over a Noetherian scheme with a dualizing complex. The former point of view allows us to obtain an explicit construction of Neeman's extraordinary inverse image functor $f^!$ for a morphism of quasicompact semiseparated schemes $f$. The latter approach provides an expanded version of the covariant SerreGrothendieck duality theory and leads to Deligne's extraordinary inverse image functor $f^!$ (which we denote by $f^+$) for a morphism of finite type $f$ between Noetherian schemes. Semiseparated Noetherian stacks, affine Noetherian formal schemes, and indaffine indschemes (together with the noncommutative analogues) are briefly discussed in the appendices.
 Publication:

arXiv eprints
 Pub Date:
 September 2012
 arXiv:
 arXiv:1209.2995
 Bibcode:
 2012arXiv1209.2995P
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Geometry
 EPrint:
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