By Ulrich Görtz, Torsten Wedhorn
This e-book introduces the reader to trendy algebraic geometry. It provides Grothendieck's technically tough language of schemes that's the foundation of an important advancements within the final fifty years inside this region. a scientific therapy and motivation of the idea is emphasised, utilizing concrete examples to demonstrate its usefulness. a number of examples from the area of Hilbert modular surfaces and of determinantal kinds are used methodically to debate the coated concepts. therefore the reader studies that the additional improvement of the idea yields an ever higher knowing of those interesting gadgets. The textual content is complemented through many workouts that serve to examine the comprehension of the textual content, deal with extra examples, or provide an outlook on extra effects. the amount to hand is an advent to schemes. To get startet, it calls for in simple terms uncomplicated wisdom in summary algebra and topology. crucial evidence from commutative algebra are assembled in an appendix. will probably be complemented through a moment quantity at the cohomology of schemes.
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