ILU (268182)

  https://cordis.europa.eu/project/id/268182

  FP7 (2007-2013)

  Local desingularization of quasi-excellent schemes

  Marie Curie Action: "Reintegration Grants" (FP7-PEOPLE-2009-RG)

  prime numbers

  2010-10-01 Start Date (YY-MM-DD)

  2014-09-30 End Date (YY-MM-DD)

  € 100,000 Total Cost

  Description

Gabber recently proved a weak local uniformization theorem that states that for any quasi-excellent integral scheme X with a valuation v there exists an alteration Y->X (i.e. a proper generically finite morphism between integral schemes) such that v lifts to a valuation on Y with a regular center. Moreover, one can achieve that the degree of the field extension k(Y)/k(X) is coprime with a fixed prime number l invertible on X. My recent inseparable local uniformization theorem refines this when X is a variety. In this case, it suffices to consider alterations with a purely inseparable extension k(Y)/k(X). The main aim of this project is to develop in the context of general quasi-excellent schemes (including the mixed characteristic case) the technique that was used to prove the inseparable local uniformization theorem. In particular, this should lead to the following strengthening of Gabber's theorem: it suffices to consider only alterations Y->X such that k(Y) is generated over k(X) by (p_i)^n-th roots where each p_i is a prime number not invertible on X.

  Complicit Organisations

1 Israeli organisation participates in ILU.