Resolution of singularities of threefolds in positive characteristic. I.

Cossart, Vincent; Piltant, Olivier

doi:10.1016/j.jalgebra.2008.03.032

Cited by 126 publications

(100 citation statements)

References 36 publications

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“…In the preceding proof, if we can replace the alteration f by a (proper birational) resolution of singularities, then the theorem is true with integral coefficients -indeed, the extension L/E which shows up in the end of the proof is trivial when f is birational. This holds in characteristic 0 by Hironaka's resolution of singularities but also in characteristic p > 0 if X is a curve, a surface (cf [Lip78]) or a 3-fold (cf [CP09]). …”

Section: Consider the Cycle Moduleĥmentioning

confidence: 89%

Coniveau filtration and mixed motives

Déglise¹

2012

Contemporary Mathematics

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Abstract. We introduce the motivic coniveau exact couple of a scheme, in the framework of mixed motives, whose property is to universally give rise to coniveau spectral sequences through realizations. The main result is a computation of its differentials in terms of residues and transfers of mixed motives, with a formula analog to the one defining the Weil divisor of a rational function. We then show how to recover and extend classical results of Bloch and Ogus for motivic realizations.

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Section: Consider the Cycle Moduleĥmentioning

confidence: 89%

Coniveau filtration and mixed motives

Déglise¹

2012

Contemporary Mathematics

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“…Recently, there has been progress on local uniformization in positive characteristic, including the work of Cossart and Piltant [5], [6], Kuhlmann [14], Knaf and Kuhlmann [13], Spivakovsky [18], [17], Temkin [20] and Teissier [19]. Some recent progress on understanding valuations in the context of algebraic geometry has been made by Favre and Jonnson [10], Ghezzi, Hà and Kascheyeva [15], Vaquié [21] and others.…”

Section: Theorem 11 (Zariski) -Suppose That R Is a Regular Local Rimentioning

confidence: 99%

Formal prime ideals of infinite value and their algebraic resolution

Cutkosky¹,

ElHitti²

2011

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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“…Vincent Cossart and Olivier Piltant have been able to resolve singularities of threefolds in any characteristic [9,10] and seem to have made progress on the arithmetic case. Cossart, Uwe Jannsen, and Shuji Saito [8] have rewritten Hironaka's resolution of surfaces in positive and mixed characteristic in its most general and strongest form to date.…”

Section: 3mentioning

confidence: 99%