Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

4 results

  • 5 - Theorem of the Base

  • Edited by Pieter Belmans, Université du Luxembourg, Wei Ho, University of Michigan, Ann Arbor, Aise Johan de Jong, Columbia University, New York
  • Book:
    Stacks Project Expository Collection
    Published online:
    06 October 2022
    Print publication:
    27 October 2022, pp 163-193

  • Summary

    We explain a proof of the Theorem of the Base: the Neron– Severi group of a proper variety is a finitely generated abelian group. We discuss, quite generally, the Picard functor and its torsion and identity components. We study representability and finiteness properties of the Picard functor, both absolutely and in families. Along the way, we streamline the original proof by using alterations, and we discuss some examples of peculiar Picard schemes.

  • Undecidability of representability as binary relations

  • Robin Hirsch, Marcel Jackson
  • Journal:
    The Journal of Symbolic Logic / Volume 77 / Issue 4 / December 2012
    Published online by Cambridge University Press:
    12 March 2014, pp. 1211-1244
    Print publication:
    December 2012

  • In this article we establish the undecidability of representability and of finite representability as algebras of binary relations in a wide range of signatures. In particular, representability and finite representability are undecidable for Boolean monoids and lattice ordered monoids, while representability is undecidable for Jónsson's relation algebra. We also establish a number of undecidability results for representability as algebras of injective functions.

  • Representability of derived stacks

  • J.P. Pridham
  • Journal:
    Journal of K-Theory / Volume 10 / Issue 2 / October 2012
    Published online by Cambridge University Press:
    31 January 2012, pp. 413-453
    Print publication:
    October 2012

  • Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify for many applications. Provided a derived analogue of Schlessinger's condition holds, the theorem reduces to verifying conditions on the underived part and on cohomology groups. Another simplification is that functors need only be defined on nilpotent extensions of discrete rings. Finally, there is a pre-representability theorem, which can be applied to associate explicit geometric stacks to dg-manifolds and related objects.