Segal conjecture fails for truncated polynomial algebras over higher chromatic local fields, causing Lichtenbaum-Quillen property to fail while weak redshift conjecture holds.
Schlank, and Alle Yuan, The Chromatic Nullstellensatz , Annals of Mathematics (to appear)
2 Pith papers cite this work. Polarity classification is still indexing.
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Compiles a list of equivalent formulations of Hilbert's Nullstellensatz in infinite dimensions and proves persistence of the strong Nullstellensatz in large polynomial rings.
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Algebraic K-theory of finite algebras over higher local fields
Segal conjecture fails for truncated polynomial algebras over higher chromatic local fields, causing Lichtenbaum-Quillen property to fail while weak redshift conjecture holds.
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Infinite Versions of Hilbert's Nullstellensatz
Compiles a list of equivalent formulations of Hilbert's Nullstellensatz in infinite dimensions and proves persistence of the strong Nullstellensatz in large polynomial rings.