ILU

Local desingularization of quasi-excellent schemes

Coordinatore	THE HEBREW UNIVERSITY OF JERUSALEM.    more  Organization address address: GIVAT RAM CAMPUS city: JERUSALEM postcode: 91904 contact info Titolo: Ms. Nome: Hani Cognome: Ben Yehuda Email: send email Telefono: 97226586618 Fax: +972 2 6513205
Nazionalità Coordinatore	Israel [IL]
Totale costo	100˙000 €
EC contributo	100˙000 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2010-RG
Funding Scheme	MC-IRG
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-10-01   -   2014-09-30

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	THE HEBREW UNIVERSITY OF JERUSALEM.  Organization address address: GIVAT RAM CAMPUS city: JERUSALEM postcode: 91904 contact info Titolo: Ms. Nome: Hani Cognome: Ben Yehuda Email: send email Telefono: 97226586618 Fax: +972 2 6513205	IL (JERUSALEM)	coordinator	100˙000.00

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 Obiettivo del progetto (Objective)

'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.'