By Jayce Getz, Mark Goresky
Within the Seventies Hirzebruch and Zagier produced elliptic modular varieties with coefficients within the homology of a Hilbert modular floor. They then computed the Fourier coefficients of those types by way of interval integrals and L-functions. during this publication the authors take another method of those theorems and generalize them to the environment of Hilbert modular types of arbitrary measurement. The method is conceptual and makes use of instruments that weren't to be had to Hirzebruch and Zagier, together with intersection homology concept, homes of modular cycles, and base swap. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular types are provided either within the classical and adèlic settings. The booklet should still offer a starting place for impending related questions for different in the neighborhood symmetric areas.
Read or Download Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change (Progress in Mathematics) PDF
Best Algebraic Geometry books
Algebraic topology is a uncomplicated a part of smooth arithmetic, and a few wisdom of this zone is necessary for any complicated paintings when it comes to geometry, together with topology itself, differential geometry, algebraic geometry, and Lie teams. This booklet offers an in depth remedy of algebraic topology either for academics of the topic and for complicated graduate scholars in arithmetic both focusing on this region or carrying on with directly to different fields.
First textbook-level account of easy examples and strategies during this quarter. appropriate for self-study via a reader who is familiar with a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yank Mathematical Society, in addition to a winning Springer writer.
Grothendieck’s attractive idea of schemes permeates glossy algebraic geometry and underlies its functions to quantity conception, physics, and utilized arithmetic. this easy account of that idea emphasizes and explains the common geometric options in the back of the definitions. within the ebook, innovations are illustrated with primary examples, and specific calculations express how the structures of scheme idea are performed in perform.
This vintage textual content, written by means of one of many most effective mathematicians of the twentieth century, is now on hand in a low-budget paperback version. Exposition is headquartered at the foundations of affine geometry, the geometry of quadratic kinds, and the constitution of the overall linear crew. Context is broadened by way of the inclusion of projective and symplectic geometry and the constitution of symplectic and orthogonal teams.
Extra info for Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change (Progress in Mathematics)