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DTSTART:20161030T020000
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UID:calendar.46351.field_date.0@mathematics.huji.ac.il
DTSTAMP:20210309T040458Z
CREATED:20171203T154726Z
DESCRIPTION:Date: \n\n2:00pm to 3:00pm\n\n\nSee also: Number Theory & Alg
ebraic Geometry\, Events & Seminars\, SeminarsLocation: \n\nRos Building\,
70A\n\n\nAbstract: In modern algebraic geometry we encounter the notion o
f derived intersection of subschemes. This is a sophisticated way to encod
e what happens when two subschemes Y_1 and Y_2 of a given scheme X interse
ct non-transversely. The classical intersection multiplicity can be extrac
ted from the derived intersection. \nWhen the ambient scheme X is affine\,
it is not too hard to describe the derived intersection\, by taking flat
DG ring resolutions of the structure sheaves of the subschemes Y_1 or Y_2.
This also works when the scheme X is quasi-projective. However\, derived
intersections in more general schemes X could only be treated using the ve
ry difficult homotopical methods of derived algebraic geometry. \nSeveral
months ago I discovered a 'cheap' way to construct flat resolutions of sh
eaves of rings. The resolutions are by semi-pseudo-free sheaves of DG ring
s. The main advantage is that the geometry does not change: all the action
takes place on the original topological space X.\nUsing semi-pseudo-free
resolutions it is possible to produce derived intersections as above. It i
s also possible to get a direct presentation of the cotangent complex of a
scheme (at least in characteristic 0). Presumably the derived adic comple
tion of Shaul\, so far studied only in the affine case\, could be globaliz
ed using our our methods. \nLastly\, the semi-pseudo-free resolutions giv
e rise to a congruence on the category of sheaves of commutative DG rings
on the space X\, that we call relative quasi-homotopy. The functor from th
e homotopy category to the derived category turns out to be a faithful rig
ht Ore localization. This fact gives tight control on the derived category
. It should be noted that in this situation there does not seem to exist a
Quillen model structure\, so the traditional approaches would fail.\nIn t
he talk I will explain the various ideas listed above. More details can be
found in the eprint arxiv:1608.04265.
DTSTART;TZID=Asia/Jerusalem:20161212T140000
DTEND;TZID=Asia/Jerusalem:20161212T150000
LAST-MODIFIED:20191103T090235Z
SUMMARY:NT&AG: Amnon Yekutieli (BGU)\, 'The Derived Category of Sheaves of
Commutative DG Rings'
URL;TYPE=URI:https://mathematics.huji.ac.il/event/ntag-amnon-yekutieli-bgu-
derived-category-sheaves-commutative-dg-rings
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