EXPOSITIO

A home for expository scholarship

Expositio is a repository for expository papers in a wide range of academic disciplines, supporting preprints, revisions, optional peer review, saved papers, and overlay journals.

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What is Expositio?

A public repository for expository academic papers, with an integrated scholarly record.

Expositio is a place to read and cite expository work. Papers are published as stable, citable records, while remaining connected to later versions, editorial decisions, and related context.

Some papers are early drafts; others have been peer reviewed or formally published. Each paper remains readable on its own, while preserving the history behind it.

The result is both a reading room and a record: a place to browse by field, read papers in stable form, and follow their development over time.

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(Co)homology theory in algebraic geometry

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Mathematics Algebraic geometry (Co)homology theory in algebraic geometry
Domain: Mathematics × Branch: Algebraic geometry × Branch: (Co)homology theory in algebraic geometry ×

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The Fundamental Theorem of Calculus, Green's theorem, the classical Stokes theorem, and the divergence theorem each relate differentiation on a region to integration on its boundary. This paper develops the language of smooth manifolds and differential forms in which these r…

Mathematics / Global analysis, analysis on manifolds Mathematics / Algebraic geometry Mathematics / Differential geometry Mathematics / Linear and multilinear algebra; matrix theory
Mathematics > Global analysis, analysis on manifolds > de Rham theory in global analysis Primary
Mathematics > Algebraic geometry > de Rham cohomology and algebraic geometry
Mathematics > Differential geometry > Integral geometry; differential forms, currents, etc.
Mathematics > Linear and multilinear algebra; matrix theory > Exterior algebra, Grassmann algebras