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Progress in Mathematics

De Rham Cohomology of Differential Modules on Algebraic Varieties

Authors: André, Yves, Baldassarri, Francesco, Cailotto, Maurizio

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  • Simplifies the approach to birational properties of connections, based on a formal analysis of singularities at infinity
  • Features a discussion on the stability of properties of connections based on higher direct images under a smooth morphism, only using basic tools of coherent cohomology
  • Presents a unified approach to GAGA-type theorems in De Rham cohomology covering both complex and $p$-adic analytifications
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eBook 42,79 €
85,59 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-39719-7
  • Digitally watermarked, DRM-free
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  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 51,99 €
103,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-39718-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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About this book

This is the revised second edition of the well-received book by the first two authors. It offers a systematic treatment of the theory of vector bundles with integrable connection on smooth algebraic varieties over a field of characteristic 0. Special attention is paid to singularities along divisors at infinity, and to the corresponding distinction between regular and irregular singularities. The topic is first discussed in detail in dimension 1, with a wealth of examples, and then in higher dimension using the method of restriction to transversal curves.

The authors develop a new approach to classical algebraic/analytic comparison theorems in De Rham cohomology, and provide a unified discussion of the complex and the p-adic situations while avoiding the resolution of singularities.

They conclude with a proof of a conjecture by Baldassarri to the effect that algebraic and p-adic analytic De Rham cohomologies coincide, under an arithmetic condition on exponents.

As used in this text, the term “De Rham cohomology” refers to the hypercohomology of the De Rham complex of a connection with respect to a smooth morphism of algebraic varieties, equipped with the Gauss-Manin connection.  This simplified approach suffices to establish the stability of crucial properties of connections based on higher direct images. The main technical tools used include: Artin local decomposition of a smooth morphism in towers of elementary fibrations, and spectral sequences associated with affine coverings and with composite functors.


Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook 42,79 €
85,59 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-39719-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 51,99 €
103,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-39718-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
De Rham Cohomology of Differential Modules on Algebraic Varieties
Authors
Series Title
Progress in Mathematics
Series Volume
189
Copyright
2020
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-39719-7
DOI
10.1007/978-3-030-39719-7
Hardcover ISBN
978-3-030-39718-0
Series ISSN
0743-1643
Edition Number
2
Number of Pages
XIV, 241
Topics