Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-17T14:44:27.577Z Has data issue: false hasContentIssue false

III. - Differential Algebraic Groups and the Number of Countable Differentially Closed Fields

Published online by Cambridge University Press:  24 March 2017

David Marker
Affiliation:
University of Illinois, Chicago
Margit Messmer
Affiliation:
University of Illinois, Urbana-Champaign
Anand Pillay
Affiliation:
University of Illinois, Urbana-Champaign
Anand Pillay
Affiliation:
University of Notre Dame
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Borel, A., Linear Algebraic Groups, Springer 1991.
Buium, A., Differential Algebraic Groups of Finite Dimension, Springer Lecture Notes 1506, 1992.
Buium, A., Differential polynomial functions on algebraic varieties I: Differential algebraic groups, American Journal of Mathematics, 1993.Google Scholar
Cassidy, Ph., Differential algebraic groups, American Journal of Mathematics, 94 (1972), 891–954.Google Scholar
Cassidy, Ph., The classification of semisimple differential algebraic groups, J. Algebra, 121 (1990), 169–238.Google Scholar
Hrushovski, E., Locally modular regular types, in Classification Theory, ed. Baldwin, J., Lecture Notes in Math. 1292, 1987.
Hrushovski, E. and Pillay, A., Weakly normal groups, Logic Colloquium ’85, North-Holland, 1987.
Hrushovski, E. and Sokolovic, Z., Minimal subsets of differentially closed fields, preprint 1994.
Hrushovski, E. and Zilber, B., Zariski geometries, to appear in Journal of A.M.S.
Lang, S., Introduction to Algebraic Geometry, Interscience, New York, 1959.
Lascar, D., Stability in Model Theory, Longman, 1987.
Manin, Yu., Rational points of algebraic curves over function fields, AMS Translations, Ser. II 50 (1966), 189–234.Google Scholar
Marker, D., Model theory of differential fields, this volume.
Pillay, A., Differential algebraic group chunks, Journal of Symbolic Logic, 55 (1990), 1138–1142.Google Scholar
Pillay, A., Some foundational questions concerning differential algebraic groups, preprint 1994.
Pillay, A., Geometrical stability theory, to appear, Oxford University Press.
Poizat, B., Groupes Stables, Nur al-Mantiq wal-Ma'rifah, Paris 1987.
Rosenlicht, M., Extensions of vector groups by abelian varieties, American Journal of Mathematics, 80 (1958), 685–714.Google Scholar
Shafarevich, I. R., Basic Algebraic Geometry, Springer, 1977.
Shelah, S., Harrington, L. and Makkai, M., A proof of Vaught's conjecture for ω-stable theories, Israel Journal of Mathematics, 49 (1984), 259–278.Google Scholar
Silverman, J., Arithmetic of Elliptic Curves, Springer, 1987

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×