Valued fields with finitely many defect extensions of prime degree

Autor(es)

Kuhlmann, Franz-Viktor

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF ALGEBRA AND ITS APPLICATIONS; v. 21, n. 03, p. 18-pg., 2022-03-01.

Resumo

We prove that a valued field of positive characteristic p that has only finitely many distinct Artin-Schreier extensions (which is a property of infinite NTP2 fields) is dense in its perfect hull. As a consequence, it is a deeply ramified field and has p-divisible value group and perfect residue field. Further, we prove a partial analogue for valued fields of mixed characteristic and observe an open problem about 1-units in this setting. Finally, we fill a gap that occurred in a proof in an earlier paper in which we first introduced a classification of Artin-Schreier defect extensions. (AU)

• Processo FAPESP: 17/17835-9 - As relações entre geometria tórica, teoria de blow-ups locais e teoria de ramificação e suas applicações em teoria das valorizações
• Beneficiário: Josnei Antonio Novacoski
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores