scholarly journals Semisimple super Tannakian categories with a small tensor generator

2015 ◽  
Vol 276 (1) ◽  
pp. 229-248 ◽  
Author(s):  
Thomas Krämer ◽  
Rainer Weissauer
Keyword(s):  
Tannakian Categories

scholarly journals Graded and filtered fiber functors on Tannakian categories

2013 ◽  
Vol 14 (1) ◽  
pp. 87-130 ◽  
Author(s):  
Paul Ziegler
Keyword(s):  
Base Scheme ◽  
Tannakian Categories

AbstractWe study fiber functors on Tannakian categories which are equipped with a grading or a filtration. Our goal is to give a comprehensive set of foundational results about such functors. A main result is that each filtration on a fiber functor can be split by a grading fpqc-locally on the base scheme.

scholarly journals On the Structure of Affine Flat Group Schemes Over Discrete Valuation Rings, II

2020 ◽  
Author(s):  
Phùng Hô Hai ◽  
João Pedro dos Santos
Keyword(s):  
Discrete Valuation Ring ◽  
Free Module ◽  
Galois Groups ◽  
Affine Group ◽  
Group Schemes ◽  
Infinite Type ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
D Modules ◽  
Tannakian Categories

Abstract In the first part of this work [ 12], we studied affine group schemes over a discrete valuation ring (DVR) by means of Neron blowups. We also showed how to apply these findings to throw light on the group schemes coming from Tannakian categories of $\mathcal{D}$-modules. In the present work, we follow up this theme. We show that a certain class of affine group schemes of “infinite type,” Neron blowups of formal subgroups, are quite typical. We also explain how these group schemes appear naturally in Tannakian categories of $\mathcal{D}$-modules. To conclude, we isolate a Tannakian property of affine group schemes, named prudence, which allows one to verify if the underlying ring of functions is a free module over the base ring. This is then successfully applied to obtain a general result on the structure of differential Galois groups over complete DVRs.

scholarly journals Differential Tannakian categories

2009 ◽  
Vol 321 (10) ◽  
pp. 3043-3062 ◽  
Author(s):  
Alexey Ovchinnikov
Keyword(s):  
Tannakian Categories

scholarly journals On certain Tannakian categories of integrable connections over Kähler manifolds

2021 ◽  
pp. 1-28
Author(s):  
Indranil Biswas ◽  
João Pedro dos Santos ◽  
Sorin Dumitrescu ◽  
Sebastian Heller
Keyword(s):  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Tannakian Categories

scholarly journals Which abelian tensor categories are geometric?

2018 ◽  
Vol 2018 (734) ◽  
pp. 145-186 ◽  
Author(s):  
Daniel Schäppi
Keyword(s):  
Characteristic Zero ◽  
Intrinsic Properties ◽  
Tensor Categories ◽  
Projective Varieties ◽  
Coherent Sheaves ◽  
Geometric Objects ◽  
Necessary And Sufficient ◽  
Tannaka Duality ◽  
Tannakian Categories

AbstractFor a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a characterization of tensor categories in the image of this embedding.However, this notion requires additional structure to be present, namely a fiber functor. For the case of classical Tannakian categories in characteristic zero, Deligne has found intrinsic properties—expressible entirely within the language of tensor categories—which are necessary and sufficient for the existence of a fiber functor. In this paper we generalize Deligne’s result to weakly Tannakian categories in characteristic zero. The class of geometric objects whose tensor categories of quasi-coherent sheaves can be recognized in this manner includes both the gerbes arising in classical Tannaka duality and more classical geometric objects such as projective varieties over a field of characteristic zero.Our proof uses a different perspective on fiber functors, which we formalize through the notion of geometric tensor categories. A second application of this perspective allows us to describe categories of quasi-coherent sheaves on fiber products.

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