Descent theory: A survey on some of its algebraic, categorical and topological aspects.

Scriptie/Masterproef: Master's Thesis

Samenvatting

Abstract (English). This thesis is centered around descent theory, with an emphasis on descent for rings
and modules. The starting point is the affine version of Grothendieck’s faithfully flat descent theorem, with
the underlying idea of embedding this into more recent literature. The first chapter discusses alternative
intepretations of non-commutative descent data in terms of flat connections and symmetry operators. These
are intertwined with aspects of Hopf-Galois- and coring theory, so as to give a proper image of how descent
theory stands in relation to the larger module-theoretic framework. The second chapter adopts a more categorical approach by means of monads and fibered categories. Reformulating descent in terms of monad language will prove fruitful for reconsidering some of the results from the first chapter, but also leads towards
more general descent methods. This culminates in the Benabou-Roubaud theorem, giving a compatibility
between monadic descent techniques and descent with respect to fibrations.
Datum prijs29 jun 2023
Originele taalEnglish

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