## MathsNet: Research Student Directory

Name | Tanania, Fabio |
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Group | Algebra and Analysis |

Room | C32, Maths |

Telephone | +44 (0) 115 [direct dial] |

Thesis Title | Cohomology theories in Algebraic Geometry |

Thesis Abstract | After the groundbreaking works of V. Voevodsky, it became possible to work with algebraic varieties by completely topological methods. An important role in this context is played by the so-called Generalized Cohomology Theories. This includes classical algebraic K-theory, but also a rather modern (and more universal) Algebraic Cobordism theory. The study of such theories and cohomological operations on them is a fascinating subject. It has many applications to the classical questions from algebraic geometry, quadratic form theory, and other areas. One can mention, for example: the Rost degree formula, the problem of smoothing algebraic cycles, and u-invariants of fields. This is a new and rapidly developing area that offers many promising directions of research. |

School contact information | School of Mathematical Sciences University of Nottingham University Park Nottingham, NG7 2RD UK Tel: +44 (0) 115 951 4949 Fax: +44 (0) 115 951 4951 |