Florian Pop: Papers

Recent manuscripts (submitted):

• A Linear Variant of GT,
  (with A. Topaz)
  arXiv.pdf

• On a Conjecture of Colliot-Thélène,
  pdf

• Reconstruction of Function Fields from their pro-l Abelian divisorial inertia,
  arXiv-pdf

Publications:

• Characterizing every finitely generated field by a single field axiom,
  (with Ph. Dittmann)
  arXiv-pdf
  Annals of Math. 198 (2023), 1-26.

• On the Pythagoras number of function fields of curves over number fields,
  pdf
  Israel J. Math. to appear (2023)

• Little survey on I/OM and its Variants and their relation to (variants of) GT,
  pdf
  Topology and its Applications 313 (15 May 2022), 107993

• A comparison between obstructions to local-global principles over semi-global fields,
  (with D. Harbater, J. Hartmann and V. Karemaker)
  arXiv-pdf
  in: Abelian Varieties and Number Theory; eds. M. Jarden and T. Shaska;
  Contemporary Mathematics 767, pp. 135-146; AMS 2021

• Large Fields in Differential Galois Theory,
  (with A. Bachmayr, D. Harbater and J. Hartmann)
  arXiv-pdf
  J. Inst. Math. Jussieu 20 (2021), 1931-1946.

• Finite tripod variants of I/OM
  pdf
  Inventiones Math 216 (2019), 745-797.

• Elementary equivalence versus Isomorphism II
  pdf
  Algebra & Number Theory 11 (2017), 2091-2111.

• Z/p metabelian birational p-adic section conjecture for varieties
  pdf
  Compositio Math. 153 (2017), 1433--1445.

• Arithmetic in the fundamental group of a p-adic curve -On the p-adic section conjecture-
  pdf
  (with Jakob Stix)
  J. reine angew. Math. 725 (2017), 1-40.

• On the minimized decomposition theory of valuations,
  With an Appendix by Adam Topaz
  pdf
  Bull. Math. Soc. Scie. Math. Roumanie 58 (106) No. 3 (2015), 331-357.

• The Oort Conjecture on Lifting Covers of Curves
  pdf
  Annals of Math. 180 (2014), 285-322.

• Little Survey on Large Fields
  pdf
  in: Valuation Theory in Interaction, EMS Series of Congress Reports 2014;
  eds: Campillo, Kuhlmann, Teissier; pp. 432-463.

• The totally S-adic is not Hibertian (Appendix to a Bary-Soroker -- Fehm paper)
  pdf
  in: Valuation Theory in Interaction, EMS Series of Congress Reports 2014;
  eds: Campillo, Kuhlmann, Teissier; pp. 14-15.

• The Block Approximation Theorem
  pdf
  (with D. Haran and M. Jarden),
  Okayama J. Math. 55 (2013), 53-85.

• On the birational anabelian program initiated by Bogomolov I
  pdf
  Invent. Math. 187 (2012), 511-533.

• Characterization of Extremal Valued Fields
  pdf
  (with Salih Azgin and Franz-Viktor Kuhlmann),
  Proceedings of the AMS Vol 140 (2012), 1535-1547.

• The absolute Galois group of subfields of the field of totally S-adic numbers
  pdf
  (with D. Haran and M. Jarden),
  Funct. Approx. Comment. Math. 46 No 2 (2012), 205-223.

• Z/l abelian-by-central Galois theory of prime divisors
  pdf
  in: The Arithmetic of Fundamental Groups: PIA 2010,
  ed. Jakob Stix; Springer-Verlag 2012; pp. 225-244.

• Recovering fields from their decomposition graphs
  pdf
  in: Number theory, Analysis and Geometry -In memory of Serge Lang,
  eds: Goldfeld, Jorgenson, Jones, Ramakrishnan, Ribet, Tate; Springer 2012; pp. 519-594.

• Anabelian Phenomena
  pdf
  in: Non-abelian Fundamental Groups and Iwasawa Theory,
  eds: Coates, Kim, Pop, Saidi, Schneider; London Math. Society
  LNS 393, Cambridge University Press 2011; pp. 1-55.

• Henselian implies Large
  pdf (preliminary version)
  Annals of Math. 172 (2010), 2183-2195.

• Pro-l abelian-by-central Galois theory of Zariski prime divisors
  pdf (preliminary version)
  Israel J. Math. 180 (2010), 43-68.

• Inertia elements versus Frobenius elements
  pdf (preliminary version)
  Math. Annalen 438 (2010), 1005-1017.
  

• On the birational p-adic section Conjecture
  pdf (preliminary version)
  Compositio Math. 146 (2010), 621-637.

• Function fields of one variable over PAC fields
  pdf (preliminary version)
  (with Moshe Jarden)
  Documenta Math. 14 (2009), 517-523.

• Pro-p hom-form of the birational anabelian conjecture over sub-p-adic fields
  pdf (preliminary version)
  (with Scott Corry),
  J. reine angew. Math. 628 (2009), 121-128.

• The absolute Galois group of the field of totally S-adic numbers
  pdf (preliminary version)
  (with D. Haran and M. Jarden),
  Nagoya Math. Journal 194 (2009), 91-147.

• First-order characterization of function field invariants over large fields
  pdf (preliminary version)
  (with B. Poonen),
  in: Model Theory with applications to algebra and analysis,
  eds: Chatzidakis, Macpherson, Pillay, Wilkie; London Math Society
  LNS 350, Cambridge University Press 2008; pp. 255-272.

• Projective group structures as absolute Galois structures with block approximation
  pdf (preliminary version)
  (with D. Haran and M. Jarden),
  Memoirs of the AMS 189 (2007), 1-56.

• Pro-l Galois theory of Zariski prime divisors
  pdf (preliminary version)
  in: Groupes de Galois arithmetiques et differentielles,
  Seminaire et Congress, Soc. Math. de France, Vol 13 (2006); pp. 293-312.

• P-adically projective groups as absolute Galois structures
  pdf (preliminary version)
  (with D. Haran and M. Jarden),
  IMRN 2005 (2005), 1957-1995.

• On the specialization homomorphism of fundamental groups of curves in positive characteristic
  (with M. Saidi)
  in: Galois groups and Fundamental groups, ed: Schneps,
  MSRI Pub. Series 41 2003; pp.107--118.

• Classically projective groups and pseudo classically closed fields
  in: Valuation Theory and its Applications Vol. II, eds. Kuhlmann et al
  Fields Institute Communications, AMS 2003; pp. 251-283.

• Elementary equivalence versus Isomorphism
  Invent. Math. 150 (2002), 385-408.

• On Alterations and birational anabelian geometry
  in: Resolution of singularities, Birkhauser PM Series, Vol. 181,
  eds: Hauser et al, Birkhauser Verlag, Basel 2000; pp. 519--532.

• Glimpses of Grothendieck's anabelian geometry
  in: Geometric Galois Actions I, LMS LNS Vol. 242,
  eds: Schneps -- Lochak, Cambridge Univ. Press 1998; pp. 133--126.

• Embedding problems over large fields
  Annals of Math. 144 (1996), 1--34.

• Etale Galois covers of affine smooth curves
  Invent. Math. 120 (1995), 555--578.

• On Rumely's local global principle
  pdf
  with B. W. Green and P. Roquette
  Jahresbericht DMV Band 97, Heft 2 (1995), 43--74.

• On pro solvable subgroups of pro-finite free products and some applications
  Manuscripta Math. 86, Fasc. 1 (1995), 125--135.

• On the Local Skolem Property
  with B. W. Green and M. Matignon,
  J. reine angew. Math. 458 (1995), 183--199.

• On Grothendieck's conjecture of anabelian birational geometry
  Annals of Math. 138 (1994), 147--185.

• Half Riemann Existence Theorem with Galois Action
  in: Algebra and Number Theory, eds: G. Frey -- J. Ritter
  de Gruyter Proceedings in Math., Berlin - New York 1994; pp. 193-218.

• On valued function fields III -Reductions of algebraic curves-
  (with B. W. Green and M. Matignon)
  J. reine angew. Math. 432 (1992), 117--133.

• On valued function fields II -Regular functions and elements with the uniqueness property-
  (with B. W. Green and M. Matignon)
  J. reine angew. Math. 412 (1990), 128--149.

• On the Galois Theory of function fields of one variable over number fields
  J.reine angew. Math. 406 (1990), 200--218.

• On valued function fields I
  (with B. W. Green and M. Matignon)
  Manuscripta Math. 65 (1989), 357--376.

• Galoissche Kennzeichnung p-adisch abgeschlossener Körper
  J. reine angew. Math. 392 (1988), 145--175.

• An extension of the Noether-Skolem Theorem
  (with H. C. Pop)
  J. pure appl. Algebra 35 (1985), 321--328.

Some other manuscripts:

• On Bogomolov's birational anabelian program II, Manuscript 2011, 2014.
  pdf

• On I/OM, Manuscript 2012, 2014.
  pdf

• Pro-l birational anabelian geometry over alg. closed fields I, Manuscript 2003.
  dvi pdf ps
  See also: http://arxiv.org/PS_cache/math/pdf/0307/0307076.

• The birational anabelian conjecture --r e v i s i t e d--, Manuscript 2002.
  dvi pdf ps
  See also: http://www.math.leidenuniv.nl/gtem/view.php

Some old Preprints/Manuscripts:

• Summen von Quadraten in arithmetischen Funktionenkorpern
  dvi pdf ps

• Etale Galois covers of smooth affine curves II
  Manuscript, Bonn 1998.

• On Grothendieck's conjecture of anabelian birational geometry II
  Heidelberg--Mannheim Preprint Reihe Arithmetik II, No. 16, Heidelberg 1995.

• A torsion criterion for geometrically henselian fields
  (with B. W. Green and M. Matignon)
  Manuscript, Heidelberg 1995.

• The geometric case of a conjecture of Shafarevich -The abs. Gal. group of k(t) is profinite free-
  pdf
  Heidelberg--Mannheim Preprint Reihe Arithmetik, No. 8, Heidelberg 1993.

• Hilbertian fields with a universal local global principle
  pdf
  Heidelberg--Mannheim Preprint Reihe Arithmetik, No. 7, Heidelberg 1993.

• On the field of totally S-adic numbers
  Manuscript, Heidelberg 1990.

• On minimal totally wild ramified extensions of henselian fields
  Manuscript, Heidelberg 1987. Contains a basic structure result of minimal wild extensions.

• On a class of tame fields
  Manuscript, Heidelberg 1986. Contains a foundation of the theory of tame fields, subsequently developed by F.-V. Kulhmann.

  The content of the above two manuscripts will appear in Kuhlmann's Book on Valuation Theory.

• Non-archimedean k*-rings
  Manuscript, Bukarest 1983 (65 pages). Thought as a Ph.D. Thesis at the University of Bucharest.

• Commutative regular k*-rings
  INCREST Preprint series in Math. No. 64, Bucharest 1982.

• On a representation problem of Arens and Kaplansky
  INCREST Preprint series in Math. No. 49, Bucharest 1981.

Back to Florian Pop's Home Page, respectively Research.