Grothendieck Duality and Base Change

Brian Conrad (Autor)

Buch | Softcover

XII, 300 Seiten

2000 | 2000
Springer Berlin (Verlag)
978-3-540-41134-5 (ISBN)

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Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.

Introduction.- Basic compatibilities.- Duality foundations.- Proof of main theorom.- Examples: Higher direct images. Curves.- Residues and cohomology with supports.- Trace map on smooth curves.

Erscheint lt. Verlag	12.12.2000
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XII, 300 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	440 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Dualizing sheaves • Grothendieck duality • MSC 14A15 • Number Theory • residues • trace map
ISBN-10	3-540-41134-8 / 3540411348
ISBN-13	978-3-540-41134-5 / 9783540411345
Zustand	Neuware