Padova-Szczecin online seminar series
hosted by the Mathematical department of the University of Padova
organized by Giulio Peruginelli and Franz-Viktor Kuhlmann
If you wish to participate in one of the talks, please write of the talks, please send an email to
Giulio Peruginelli
or Franz-Viktor Kuhlmann to obtain the Zoom link or password. The meeting ID is 841 9717 7413.
Past talks:
Friday, July 2, 2021, 15:00:
Kęstutis
Česnavičius
gave a talk on
Valuation rings and limits of regular rings
Abstract:
For many questions in arithmetic algebraic geometry, it would be useful to know that every valuation ring is a filtered direct limit of regular rings, as follows from the local uniformization conjecture. In this talk I will review this and related questions.
Slides
Friday, June 25, 2021, 15:00:
Arpan Dutta
Department of Mathematics, IISER Mohali, India
gave a talk on
Minimal pairs and implicit constant fields
Abstract:
In this talk, we establish a connection between minimal pairs of definition and implicit constant fields for valuation transcendental extensions.
Slides
Friday, June 18, 2021, 15:00:
Dario Spirito
Dipartimento di Matematica, Universita' di Padova, Italy
gave a talk on
Using pseudo-monotone sequences to extend valuations
Abstract:
We introduce the class of pseudo-monotone sequences, a generalization of pseudo-convergent sequences, in order to generalize Ostrowski's Fundamentalsatz to valuation domains of arbitrary rank.
This is a joint work with Giulio Peruginelli.
Slides
Friday, June 11, 2021, 15:00:
Giulio
Peruginelli
Dipartimento di Matematica, Universita' di Padova, Italy
gave a talk on
Extending valuations to the field of rational functions in the spirit of
Ostrowski
Abstract:
Given a rank one valuation V on a field K, Ostrowski's approach to the study of rank one extensions of V to the field of rational functions K(X) was based on a special kind of sequences of elements of K that he introduced and called pseudo-convergent. We will review his ideas and how his method has been recently generalized to characterize extensions to K(X) of a valuation of K of any rank.
We will show some results about two relevant subspaces of the Zariski-Riemann space of valuation domains of K(X) arising from pseudo-convergent sequences.
This is joint work with Dario Spirito.
Slides
Friday, June 4, 2021, 15:00:
Anna Rzepka
Institute of Mathematics, University of Silesia at Katowice, Poland
gave a talk
On a characterization of defectless fields
Abstract:
The investigation of valued fields and related areas has shown the importance
of a better understanding of the structure of defect extensions of valued fields. An
important task is to give necessary and sufficient conditions for a valued field to admit
no defect extensions.
Ramification theoretical methods show that a central role in the issue of defect
extensions is played by towers of Galois defect extensions of prime degree. We
classify separable defect extensions of prime degree into dependent and independent
ones. We also use the classification of defect extensions to give conditions for valued
fields toadmit no defect extensions.
Further, we introduce and study several classes of valued fields, like semitame
fields, deeply ramified fields and generalized deeply ramified (gdr) fields. All the
classes under consideration can be seen as generalizations of the class of tame valued
fields. In particular, we investigate which types of defect extensions such fields
admit and give conditions for generalized deeply ramified fields to admit no defect
extensions.
This is joint work with Franz-Viktor Kuhlmann.
Slides
Friday, May 21, 2021, 15:00:
Andrei Bengus-Lasnier
Institut de Mathématiques de Jussieu - Paris Rive Gauche, France
gave a talk on
Minimal Pairs, Key Polynomials (and Diskoids)
Abstract
Slides
Last update: May 5, 2024