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2013; 140 pp; softcover
List Price: US$63
Member Price: US$50.40
Order Code: AST/357
A Tannakian category is an abelian tensor category equipped with a fiber functor and additional structures which ensure that it is equivalent to the category of representations of some affine groupoid scheme acting on the spectrum of a field extension. If we are working over an arbitrary commutative ring rather than a field, the categories of representations cease to be abelian.
The author provides a list of sufficient conditions which ensure that an additive tensor category is equivalent to the category of representations of an affine groupoid scheme acting on an affine scheme, or, more generally, to the category of representations of a Hopf algebroid in a symmetric monoidal category. In order to do this he develops a "formal theory of Tannaka duality" inspired by Ross Street's "formal theory of monads." He applies his results to certain categories of filtered modules which are used to study \(p\)-adic Galois representations.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians interested in Tannaka duality, pseudomonoids, and Hopf monoidal comonads.
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