Characteristic p methods in characteristic zero via ultraproducts

Hans Schoutens ()
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Hans Schoutens: City University of New York, Department of Mathematics

A chapter in Commutative Algebra, 2011, pp 387-420 from Springer

Abstract: Abstract In recent decades, by exploiting the algebraic properties of the Frobenius in positive characteristic, many so-called homological conjectures and intersection conjectures have been established, culminating into the powerful theory of tight closure and big Cohen–Macaulay algebras. In the present article, I give a survey of how these methods also can be applied directly in characteristic zero by taking ultraproducts, rather than through the cumbersome lifting/reduction techniques. This has led to some new results regarding rational and log-terminal singularities, as well as some new vanishing theorems. Even in mixed characteristic, we can get positive results, albeit only asymptotically.

Keywords: Local Ring; Characteristic Zero; Noetherian Ring; Regular Ring; Schubert Variety (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-6990-3_15

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DOI: 10.1007/978-1-4419-6990-3_15

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