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Derived Categories: A Quick Tour

D. Huybrechts

in Fourier-Mukai Transforms in Algebraic Geometry

Published in print:
2006
Published Online:
September 2007
ISBN:
9780199296866
eISBN:
9780191711329
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296866.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter briefly outlines the main steps in the construction of the derived category of an arbitrary abelian category. The homotopy category of complexes is considered as an intermediate step, ... More


CATEGORIES

Steve Awodey

in Category Theory

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568612
eISBN:
9780191717567
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568612.003.0001
Subject:
Mathematics, Algebra

This chapter begins with a discussion of category theory, which can be defined as the mathematical study of (abstract) algebras of functions. The functions of sets, definitions of a category, ... More


Tarski's Thesis

Gila Sher

in New Essays on Tarski and Philosophy

Published in print:
2008
Published Online:
September 2010
ISBN:
9780199296309
eISBN:
9780191712272
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296309.003.0012
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter investigates the thesis that Invariance Under Isomorphisms is a criterion of logicality (logical operators) and the roots of this criterion in Tarski. It discusses the philosophical ... More


Eisenstein Cohomology

Günter Harder and A. Raghuram

in Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions: (AMS-203)

Published in print:
2019
Published Online:
September 2020
ISBN:
9780691197890
eISBN:
9780691197937
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691197890.003.0006
Subject:
Mathematics, Number Theory

This chapter provides the Eisenstein cohomology. It begins with the Poincaré duality and maximal isotropic subspace of boundary cohomology. Here, the chapter considers the compatibility of duality ... More


Diamonds associated with adic spaces

Peter Scholze and Jared Weinstein

in Berkeley Lectures on p-adic Geometry: (AMS-207)

Published in print:
2020
Published Online:
January 2021
ISBN:
9780691202082
eISBN:
9780691202150
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691202082.003.0010
Subject:
Mathematics, Geometry / Topology

This chapter focuses on diamonds associated with adic spaces. The goal is to construct a functor which forgets the structure morphism to Spa Zp, but retains topological information. The chapter ... More


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