[Turkmath:6954] Mimar Sinan Matematik Bölümü Genel Seminerleri - 9 Nisan 2010

[Safak Ozden]

Mimar Sinan Güzel Sanatlar Üniversitesi

Matematik Bölümü Genel Seminerleri


 Additive reducts of valued fields in positive characteristic

*
*

*Konuşmacı:*

Gönenç Onay

(Universite Paris 7)


First order theories of valued fields in characteristic $p>0$ are less
explored then their analogous in characteristic 0. For example, despite
strong analogies with field of p-adic numbers $Q_p$, we know very few about
the complete theory of Laurent series field $F_q((t))$. In addition, such
results can include strong assumptions like resolution of singularities. One
idea introduced by Lou van den Dries is to study a such field K as a module
over the ring of additive polynomials. A polynomial over $K$ is said to be
additive if it is additive as a map on the algebraic closure of $K$. Such
polynomials has a -*non commutativ*e- ring structure under addition and
composition.


In this talk, after presenting  motivations arising from valued fields and
recalling some basic notions from model theory I'll will define a
class of "valued
modules" and classify  all $C$-minimal such ones. Here $C$-minimal means
that every definable 1-dimensional subset is a finite Boolean combination of
balls with respect to valuation topology. As an example,  $C$-minimal valued
fields are algebraically closed.

This talk is intended to be accessible to students with undergraduate
algebra background.

*Yer:* 408 No'lu Amfi

MSGSÜ Fen Edebiyat Fakültesi (Beşiktaş)

*Zaman:*  9 Nisan 2010 Cuma, 15:00
-------------- sonraki bölüm --------------
Bir HTML eklentisi temizlendi...
URL: http://yunus.listweb.bilkent.edu.tr/pipermail/turkmath/attachments/20100406/07002b6c/attachment.htm