Virtual Cartier divisors and blow-ups

Abstract

We prove a universal property for blow-ups in regularly immersed subschemes, based on a notion we call "virtual effective Cartier divisor". We also construct blow-ups of quasi-smooth closed immersions in derived algebraic geometry.

19 pages; version 2 adds a comparison between virtual and generalized Cartier divisors, a new section on simultaneous blow-ups in multiple centres and blow-ups in unramified centres, and a new co-author

References in corpus (6)

• Algebraic K-theory and descent for blow-ups
• K-theory and G-theory of derived algebraic stacks
• Algebraic K-theory of quasi-smooth blow-ups and cdh descent
• Precobordism and cobordism
• Categorical Milnor squares and K-theory of algebraic stacks
• Algebraic Spivak's theorem and applications

Cited by in corpus (3)

• Fundamental classes in motivic homotopy theory
• Equivariant Grothendieck-Riemann-Roch and localization in operational K-theory
• A categorification of the quantum Lefschetz principle