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Samaria Montenegro

Publications and source records attributed to Samaria Montenegro.

6 recordsLinked to original sources
arXiv2023

Pseudo T-closed fields

Pseudo algebraically closed, pseudo real closed, and pseudo $p$-adically closed fields are examples of unstable fields that share many similarities, but have mostly been studied separately. In this text, we propose a unified framework for studying them: the class of pseudo $T$-closed fields, where $T$ is an enriched theory of fields. These fields verify a "local-global" principle for the existence of points on varieties with respect to models of $T$. This approach also enables a good description of some fields equipped with multiple $V$-topologies, particularly pseudo algebraically closed fields with a finite number of valuations. One important result is a (model theoretic) classification result for bounded pseudo $T$-closed fields, in particular we show that under specific hypotheses on $T$, these fields are NTP$_2$ of finite burden.

math.LO↗
arXiv2021

Groups definable in partial differential fields with an automorphism

In this paper we study groups definable in existentially closed partial differential fields of characteristic 0 with an automorphism which commutes with the derivations. In particular, we study Zariski dense definable subgroups of simple algebraic groups, and show an analogue of Phyllis Cassidy's result for partial differential fields. We also show that these groups have a smallest definable subgroup of finite index.

math.LO↗
arXiv2019

Imaginaries, invariant types and pseudo p-adically closed fields

In this paper, we give a very general criterion for elimination of imaginaries using an abstract independent relation. We also study germs of definable functions at certain well-behaved invariant types. Finally we apply these tools to the elimination of imaginaries in bounded pseudo-p-adically closed fields.

math.LO↗
arXiv2018

Stabilizers, groups with f-generics in NTP2 and PRC fields

In this paper we develop three different subjects. We study and prove alternative versions of Hrushovski's "Stabilizer Theorem", we generalize part of the basic theory of definably amenable NIP groups to NTP2 theories, and finally, we use all this machinery to study groups with f-generic types definable in bounded PRC fields.

math.LO↗
arXiv2016

Pseudo real closed field, pseudo p-adically closed fields and NTP2

The main result of this paper is a positive answer to the Conjecture 5.1 by A. Chernikov, I. Kaplan and P. Simon: If M is a PRC field, then Th(M) is NTP_2 if and only if M is bounded. In the case of PpC fields, we prove that if M is a bounded PpC field, then Th(M) is NTP_2. We also generalize this result to obtain that, if M is a bounded PRC or PpC field with exactly n orders or p-adic valuations respectively, then Th(M) is strong of burden n. This also allows us to explicitly compute the burden of types, and to describe forking.

math.LO↗