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Inventiones mathematicae

, Volume 211, Issue 2, pp 523–577 | Cite as

Algebraic K-theory and descent for blow-ups

  • Moritz KerzEmail author
  • Florian Strunk
  • Georg Tamme
Article

Abstract

We prove that algebraic K-theory satisfies ‘pro-descent’ for abstract blow-up squares of noetherian schemes. As an application we derive Weibel’s conjecture on the vanishing of negative K-groups.

Notes

Acknowledgements

Ofer Gabber suggested to us to use derived algebraic geometry in order to generalize Thomason’s calculation of the K-theory of a blow-up in a regularly immersed center, see Sect. 3. We would like to thank him for this essential remark. We would like to thank Matthew Morrow for several helpful discussions about his work on pro-calculations in K-theory. Finally, we thank the referee for his or her careful reading of the manuscript and several comments to improve the presentation.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany

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