Completion and torsion over commutative DG rings
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Completion and torsion over commutative DG rings
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Completion and torsion over commutative DG rings
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Israel Journal of Mathematics
ISSN
0021-2172
e-ISSN
—
Svazek periodika
2019
Číslo periodika v rámci svazku
2
Stát vydavatele periodika
IL - Stát Izrael
Počet stran výsledku
58
Strana od-do
531-588
Kód UT WoS článku
000480562000002
EID výsledku v databázi Scopus
2-s2.0-85070370803