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Local desingularization of quasi-excellent schemes

Objetivo

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.

Convocatoria de propuestas

FP7-PEOPLE-2010-RG
Consulte otros proyectos de esta convocatoria

Coordinador

THE HEBREW UNIVERSITY OF JERUSALEM
Aportación de la UE
€ 100 000,00
Dirección
EDMOND J SAFRA CAMPUS GIVAT RAM
91904 Jerusalem
Israel

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Tipo de actividad
Higher or Secondary Education Establishments
Contacto administrativo
Hani Ben Yehuda (Ms.)
Enlaces
Coste total
Sin datos