Jan 25, 2012

Scheme theory over the field of characteristic one

Posted by in Deitmar2004, media, Tits1957, undergraduate No comments

Second part in a series which I gave at a seminar in Ghent (April 28, 2011): “Scheme theory over the field of characteristic one”. (The first part being “Introduction to Absolute Arithmetic”.)

Sep 21, 2011

Introduction to Absolute Arithmetic

Posted by in Tits1957, undergraduate No comments

This is part 1 of a series of two lectures which I recently gave at a seminar in Ghent (April 28, 2011): “Introduction to Absolute Arithmetic”.

Feb 11, 2011


Posted by in levels, library, media, papers, research No comments

Here is the recently published paper “The hyperring of adèle classes” (by Connes and Consani). ConnesConsani2011

Jan 30, 2009


Posted by in library, Marcolli2009, news No comments

Matilde Marcolli: Cyclotomy and endomotives; arXived on January 20th, 2009: arXiv:0901.3167v1.

Dec 1, 2008

un dessin d’enfance

Posted by in Manin2008, news 1 comment

Slides are available of a talk given last week in Reims on Manin’s analytic F_un-geometry.

Oct 31, 2008

Halloween-talk : prep-notes

Posted by in KapranovSmirnov, Kurokawa2005, Manin1995, Manin2006, Manin2008, news No comments

The prep-notes for the halloween-talk on “F_un and other ghost stories” at the Arts are available.

Oct 28, 2008

Consani on F_un

Posted by in Connes-C-M-2008, webcasts No comments

Katia Consani gave a talk “On the notion of geometry over F_un” at the Fields institute.

Oct 13, 2008

noncommutative F_un geometry (1)

Posted by in Connes-Consani2008, research 4 comments

It is perhaps surprising that Alain Connes and Katia Consani, two icons of noncommutative geometry, restrict themselves to define commutative algebraic geometry over the field with one element. Remains the fact that their approach screams for a noncommutative extension.

Oct 10, 2008

Connes-Consani for undergraduates (3)

Posted by in Connes-Consani2008, undergraduate 1 comment

Alain Connes and Katia Consani arXived the paper “On the notion of geometry over F_un” in which they refine and simplify Soule’s approach. This series tries to explain their construction to non-specialists in algebraic geometry.

Oct 9, 2008

Gadgets a la Soulé

Posted by in graduate, Soule2004 3 comments

Inspired by the equivalent definition of a scheme as a particular kind of functor, Soulé gives his definition of a gadget over F_un as a couple consisting on a functor, that takes the rôle of the functor of points, and an algebra, which encodes a ‘topology at infinity’ and gives us the extra information that is missing in the functor.