Completion and torsion over commutative DG rings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10400358" target="_blank" >RIV/00216208:11320/19:10400358 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nJ5~nYPOy1" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=nJ5~nYPOy1</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-019-1866-6" target="_blank" >10.1007/s11856-019-1866-6</a>

Result language
angličtina
Original language name
Completion and torsion over commutative DG rings
Original language description
Let CDG(cont) be the category whose objects are pairs (A, (a) over bar), where A is a commutative DG-algebra and (a) over bar subset of H-0(A) is a finitely generated ideal, and whose morphisms f : (A, (a) over bar) -> (B, (b) over bar) are morphisms of DG-algebras A -> B, such that (H0(f)((a) over bar)) subset of (b) over bar. Letting Ho(CDG(cont)) be its homotopy category, obtained by inverting adic quasi-isomorphisms, we construct a functor L. : Ho(CDG(cont)) -> Ho(CDG(cont)) which takes a pair (A, (a) over bar) into its non-abelian derived (a) over bar -adic completion. We show that this operation has, in a derived sense, the usual properties of adic completion of commutative rings, and that if A = H-0(A) is an ordinary noetherian ring, this operation coincides with ordinary adic completion. As an application, following a question of Buchweitz and Flenner, we show that if k is a commutative ring, and A is a commutative k-algebra which is a-adically complete with respect to a finitely generated ideal a subset of A, then the derived Hochschild cohomology modules Ext(A circle times LkA)(n) (A, A) and the derived complete Hochschild cohomology modules Ext(A (circle times) over cap LkA)(n) (A, A) coincide, without assuming any finiteness or noetherian conditions on k, A or on the map k -> A.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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