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Concept

Sheaf (mathematics)

Related courses (11)

MATH-506: Topology IV.a - Cohomology rings

Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative algebra. We study an algebraic version, namely group coho ...

MATH-510: Algebraic geometry II - schemes and sheaves

The aim of this course is to learn the basics of the modern scheme theoretic language of algebraic geometry. ...

MATH-410: Riemann surfaces

This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex domains under discontinuous group actions, as algebraic ...

MATH-647: Topics on the Euler and Navier-Stokes equations

This topics course focuses on recent and classical fundamental results on the Euler and Navier-Stokes equations, such as global existence of weak solutions, (non)uniqueness results, blow-ups, partial regularity, anomalous dissipation. ...

MATH-658: Vanishing cycles and perverse sheaves

This course will explain the theory of vanishing cycles and perverse sheaves. We will see how the Hard Lefschetz theorem can be proved using perverse sheaves. If we have more time we will try to see the decomposition theorem and how to categorify certain p ...

MATH-657: Deformation Theory

We will study classical and modern deformation theory of schemes and coherent sheaves. Participants should have a solid background in scheme-theory, for example being familiar with the first 3 chapters of Hartshorne's 'Algebraic Geometry'. ...

MATH-643: Applied l-adic cohomology

In this course we will describe in numerous examples how methods from l-adic cohomology as developed by Grothendieck, Deligne and Katz can interact with methods from analytic number theory (prime numbers, modular forms etc...). ...

MATH-645: Young Topologists Meeting Mini-Courses

We expect these mini-courses to equip junior researchers with new tools, techniques, and perspectives for attacking a broad range of questions in their own areas of research while also inspiring students to learn more about ground-breaking advances in pure ...

MATH-473: Complex manifolds

The goal of this course is to help students learn the basic theory of complex manifolds and Hodge theory. ...

MATH-679: Group schemes

This is a course about group schemes, with an emphasis on structural theorems for algebraic groups (e.g. Barsotti--Chevalley's theorem). All the basics will be covered towards the proof of such theorem, with an estress on the modern presentation using sche ...

MATH-684: Spectral sequences

The goal of the course is to learn how to construct and calculate with spectral sequences. We will cover the construction and introductory computations of some common and famous spectral sequences. ...