Obiettivo
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.
Campo scientifico
Invito a presentare proposte
FP7-PEOPLE-2010-RG
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Meccanismo di finanziamento
MC-IRG - International Re-integration Grants (IRG)Coordinatore
91904 Jerusalem
Israele