0000000000634036

AUTHOR

Moritz Kerz

showing 2 related works from this author

Towards Vorst's conjecture in positive characteristic

2018

Vorst's conjecture relates the regularity of a ring with the $\mathbb{A}^1$-homotopy invariance of its $K$-theory. We show a variant of this conjecture in positive characteristic.

CombinatoricsMathematics - Algebraic GeometryRing (mathematics)Algebra and Number TheoryConjectureMathematics::K-Theory and HomologyMathematics - K-Theory and HomologyFOS: MathematicsK-Theory and Homology (math.KT)Algebraic Geometry (math.AG)Valuation ringMathematicsCompositio Mathematica
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The complex of words and Nakaoka stability

2005

We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka's homology stability for symmetric groups. The methods are generalized to show acyclicity in low degrees for the complex of words in "general position". Hm(§ni1;Z) = Hm(§n;Z) for n=2 > m where §n denotes the permutation group of n elements. An elementary proof of this fact has not been available in the literature. In the first section the complex C⁄(m) of abelian groups is studied which in de- gree n is freely generated by injective words of length n. The alphabet consists of m letters. The complex C⁄(m) has the only non vanishing homology in degree m (Theorem 1). This is a result of F.…

CombinatoricsMathematics (miscellaneous)Symmetric groupElementary proofAbelian groupHomology (mathematics)Permutation groupPartially ordered setInjective functionMathematicsVector spaceHomology, Homotopy and Applications
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