p-adic Differential Equations: Edition 2
Kiran S. Kedlaya
ΠΈΡΠ½Ρ 2022β―Π³. Β· Cambridge Studies in Advanced Mathematics ΠΠ½ΠΈΠ³Π°Β 199 Β· Cambridge University Press
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π°Ρ ΠΊΠ½ΠΈΠ³Π°
496
ΠΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΡΡΡΠ°Π½ΠΈΡ
reportΠΡΠ΅Π½ΠΊΠΈ ΠΈ ΠΎΡΠ·ΡΠ²Ρ Π½Π΅ ΠΏΡΠΎΠ²Π΅ΡΠ΅Π½Ρ. ΠΠΎΠ΄ΡΠΎΠ±Π½Π΅Π΅β¦
ΠΠ± ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΊΠ½ΠΈΠ³Π΅
Now in its second edition, this volume provides a uniquely detailed study of $P$-adic differential equations. Assuming only a graduate-level background in number theory, the text builds the theory from first principles all the way to the frontiers of current research, highlighting analogies and links with the classical theory of ordinary differential equations. The author includes many original results which play a key role in the study of $P$-adic geometry, crystalline cohomology, $P$-adic Hodge theory, perfectoid spaces, and algorithms for L-functions of arithmetic varieties. This updated edition contains five new chapters, which revisit the theory of convergence of solutions of $P$-adic differential equations from a more global viewpoint, introducing the Berkovich analytification of the projective line, defining convergence polygons as functions on the projective line, and deriving a global index theorem in terms of the Laplacian of the convergence polygon.
ΠΠ± Π°Π²ΡΠΎΡΠ΅
Kiran S. Kedlaya is the Stefan E. Warschawski Professor of Mathematics at University of California, San Diego. He has published over 100 research articles in number theory, algebraic geometry, and theoretical computer science, as well as several books, including two on the Putnam competition. He has received a Presidential Early Career Award, a Sloan Fellowship, and a Guggenheim Fellowship, and been named an ICM invited speaker and a fellow of the American Mathematical Society.
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