2024 Tannakian reconstruction

Tannakian reconstruction

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August undefined, 2024

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WebOn Tannakian duality over valuation rings Torsten Wedhorn Mathematisches Institut Bonn, Beringstraße 4, 53115 Bonn, Germany ... The reconstruction problem: given a “group-like” object G (e.g., a group scheme, a gerbe, a quantum group), is it possible to recover G from the category of its rep- WebJul 30, 2011 · Doctrinal and Tannakian Reconstruction Posted by David Corfield Interest in doctrines at the Café goes right back to one of its earliest posts nearly five years ago, and even to one a few days earlier. We’ve begun to record some material at the doctrine page in nLab, but I’m sure there’s more wisdom from the blog to be extracted. fredericktown missouri news

Doctrinal and Tannakian Reconstruction The n-Category Café

WebJul 26, 2024 · Tannakian reconstruction of reductive group schemes. We give sharp criteria for when a reductive group scheme satisfies Tannakian reconstruction. When the base … WebBackground. The famous Tannakian reconstruction theorem says that an algebraic group can be recovered from its representation category. To be a bit more precise, ﬁx an algebraically closed ﬁeld k. A pre-Tannakian category is a k-linear abelian category equipped with a symmetric tensor structure satisfying some axioms. A Tannakian … WebJul 22, 2024 · 1 You can consider the Tannakian category of "finite vector bundles" in the sense of Nori, see his paper "On the representations of the fundamental group" in … blind love tom waits lyrics

A Tannakian Reconstruction Theorem for IndBanach …

Tannakian formalism - Wikipedia

Websurprisingly similar to Tannakian reconstruction; we will prove the theorem following the proof of Tannakian reconstruction (for, say, groups). The proof written in this way is similar to the one used by Riley [Ril18]. Theorem 3. Let U (A;B): ˜ !Sets the functor that evaluates a Tambara module on the object (A;B). There exists an isomorphism ... WebWe note that the introduction to Saavedra Rivano 1972 is an excellent summary of Tannakian categories, except that two changes are necessary: Theor´ eme 3 is, … blind love tom waitsWebTannakian equivalence to eventually identify Hwith the Langlands dual group G_. We begin by enumerating some of the visible properties of the category Rep k (G) for a reductive algebraic group G, as a means of motivating the statement of the Tannakian reconstruction theorem. This is an abelian, k-linear category (i.e. hom blind loyalty at work

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Tannakian reconstruction

WebTan Yankai was born on 25 January 1880 in Hangzhou during the waning decades of the Qing dynasty.He was the son of the Qing minister Tan Zhonglin.A member of Liang … WebOct 6, 2024 · Tannakian reconstruction of coalgebroids. Get access. Share. Cite. Summary. In this expository paper, we show that the Deligne–Mumford moduli space of stable curves is projective over Spec (Ζ). The proof we exposit is due to Kollár. Ampleness of a line bundle is deduced from nefness of a related vector bundle via the Ampleness Lemma, a ...

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WebJul 14, 2024 · In this short paper, we use Tannakian reconstruction techniques to prove a result that explains how to reconstruct the stacky approach to de Rham cohomology from the classical theory of algebraic... WebWe give sharp criteria for when a reductive group scheme satisfies Tannakian reconstruction. When the base scheme is Noetherian, we explicitly identify its Tannaka …

WebTannakian categories, which is the last step towards the main theorem of this book, the Tannaka-Krein duality theorem, that we introduce in Chapter 6. These last two chapters show the reader the importance of Tannakian Categories, following a very constructive introduction to these, starting with abelian categories and ending up WebFeb 4, 2024 · In a comment exchange around an answer to Is a group scheme determined by its category of representations? there arose the issue of Tannakian reconstruction for non-affine algebraic groups (e. g. abelian varieties, in particular, elliptic curves).

WebJul 14, 2024 · In this short paper, we use Tannakian reconstruction techniques to prove a result that explains how to reconstruct the stacky approach to de Rham cohomology from … WebProof. The claim is that this theorem is precisely Tannakian reconstruction for Tam-bara modules. We rst note that, by de nition, the functor U (A;B) is represented by Optic((A;B); ), …

WebTannakian reconstruction poses the following question: give necessary and su cient con-ditions on a ne category schemes X and triples (C;R;F) for the above constructions to be …

WebJan 26, 2024 · The motivation for our approach is two-fold: (1) the observation that relational schema induction is a form of Tannakian reconstruction , and (2) the fact that Tannakian reconstruction is a universal construction in the category theory sense . In this way, our theory derives from a category theory version of Tannakian reconstruction. fredericktown missouri mapWebThe Tannakian reconstruction techniques used in our paper is useful in more general situations concerning derived categories of representations, see Remark 3.0.7. 1.1 Warning This note is only about reconstruction of the stacky approach to de Rham cohomology. We do not make any claims about reconstruction of the stacks Σ,Σ′,Σ′′ from ... blind low vision tennisWebAug 1, 2024 · Details in applying the Barr-Beck monadicity theorem to Tannakian reconstruction Details in applying the Barr-Beck monadicity theorem to Tannakian reconstruction algebraic-geometry category-theory monoidal-categories monads 1,097 The Barr-Beck part of the proof is the following. blind low vision nz donationWebMar 30, 2024 · We consider now various types of size constraints on tensor categories. The Tannaka reconstruction theorem (theorem below) only assumes one of them (subexponential growth, def. ), but the others appear in the course of the proof of the theorem. finiteness (def. ) finite ⊗ \otimes-generation (def. ) subexponential growth (def. ) blind low visionWebApr 23, 2024 · On the other hand there are lots of reconstruction theorems whose gist tend to be that a scheme is determined by its (derived) category of sheaves, e.g. Tannaka dualities and the Gabriel-Rosenberg reconstruction theorem. How do these not contradict each other? algebraic-geometry sheaf-theory abelian-varieties derived-categories Share … blind low vision manurewaWebJul 29, 2024 · Classical Tannakian reconstruction recovers an affine group scheme $G$ over $k$ from the category of its linear representations over a field $k$ (as the automorphism group of the forgetful functor to the category $Vect_k$ of finite-dimensional vector spaces over $k$ .) This has many generalizations in the literature as I am slowly … blind low vision jobsWebYou can see how Tannian families moved over time by selecting different census years. The Tannian family name was found in the USA, the UK, and Scotland between 1871 and 1920. … blind low vision shop