On a noncommutative Iwasawa main conjecture for varieties over finite fields

Witte, Malte

doi:10.48550/arxiv.1004.2481

Cited by 2 publications

(2 citation statements)

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“…This is a crucial step in the proof of our main results. Note that determinant functors on Waldhausen categories have already been successfully applied in non-commutative Iwasawa theory [Wit08,Wit10], and in A 1 -homotopy theory [Eri09]. They have also been discussed in the University of Chicago's Geometric Langlands Seminar [Boy], see Remark 1.2.8.…”

Section: Introductionmentioning

confidence: 99%

On determinant functors and $K$-theory

Muro¹,

Tonks²,

Witte³

2015

Publicacions Matemàtiques

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We extend Deligne's notion of determinant functor to Waldhausen categories and (strongly) triangulated categories. We construct explicit universal determinant functors in each case, whose target is an algebraic model for the 1-type of the corresponding K-theory spectrum. As applications, we answer open questions by Maltsiniotis and Neeman on the K-theory of (strongly) triangulated categories and a question of Grothendieck to Knudsen on determinant functors. We also prove additivity theorems for low-dimensional Ktheory of (strongly) triangulated categories and obtain generators and (some) relations for various K 1 -groups. This is achieved via a unified theory of determinant functors which can be applied in further contexts, such as derivators.

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Section: Introductionmentioning

confidence: 99%

On determinant functors and $K$-theory

Muro¹,

Tonks²,

Witte³

2015

Publicacions Matemàtiques

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show abstract

“…For example, in [22], the authors study the structure of Selmer groups using syntomic cohomology for p-adic Lie extensions of fields of characteristic p containing the unique Z p -extension of the constant field. Moreover [37] provides a comprehensive study of the whole theory (including a proof of the main conjecture) in the language of schemes, for ℓ-adic extensions of a separated scheme X of finite type over the field F p e ; his proof uses K-theory, Waldhausen categories (and higher K-groups) and other cohomological tools. Another approach to the main conjecture (for Z d ℓ -extensions) is provided in [15].…”

Section: Introductionmentioning

confidence: 99%