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NCTS Seminar in Algebraic Geometry
16:00 - 17:00, January 21, 2022 (Friday)
broadcast in Room 515, Cosmology Bldg., Online seminar
(線上演講 於次震宇宙館515教室直播/收播)
Derived Blow-ups Using Rees Algebras and Virtual Cartier Divisors
Jeroen Hekking (KTH Royal Institute of technology)


The blow-up B of a scheme X in a closed subscheme Z enjoys the universal property that for any scheme X' over X such that the pullback of Z to X' is an effective Cartier divisor, there is a unique morphism of X' into B over X. It is well-known that the blow-up commutes along flat base change.
In this talk, I will discuss a derived enhancement B' of B, namely the derived blow-up, which enjoys a universal property against all schemes over X, satisfies arbitrary (derived) base-change, and contains B as a closed subscheme. To this end, we will need some elements from derived algebraic geometry, which I will review along the way. This will allow us to construct the derived blow-up as the projective spectrum of the derived Rees algebra, and state its functor of points in terms of virtual Cartier divisors, using Weil restrictions.
This is based on ongoing joint work with Adeel Khan and David Rydh.
Join Zoom Meeting
Meeting ID: 879 0868 1099
Passcode: LabBirGeom


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