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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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