Actions and Invariants of Algebraic Groups (Chapman & by Walter Ferrer Santos,Alvaro Rittatore

By Walter Ferrer Santos,Alvaro Rittatore

activities and Invariants of Algebraic teams provides a self-contained creation to geometric invariant idea that hyperlinks the fundamental concept of affine algebraic teams to Mumford's extra refined conception. The authors systematically make the most the point of view of Hopf algebra concept and the idea of comodules to simplify and compactify the various correct formulation and proofs.

The first chapters introduce the topic and overview the necessities in commutative algebra, algebraic geometry, and the idea of semisimple Lie algebras over fields of attribute 0. The authors' early presentation of the ideas of activities and quotients is helping to explain the next fabric, quite within the examine of homogeneous areas. This learn features a special therapy of the quasi-affine and affine situations and the corresponding innovations of observable and distinctive subgroups.

Among the numerous different themes mentioned are Hilbert's 14th challenge, entire with examples and counterexamples, and Mumford's effects on quotients by means of reductive teams. End-of-chapter workouts, which variety from the regimen to the quite tough, construct services in operating with the basic ideas. The Appendix additional complements this work's completeness and accessibility with an exhaustive word list of simple definitions, notation, and results.

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