Heights and Unlikely Intersections

Research Project
|
01.04.2013
- 28.02.2017

Using heights and other methods, for example tools from o-minimality, we study various problems in diophantine and arithmetic geometry. The main emphasis is on conjectures on unlikely intersections generalizing the classical Andr'e-Oort, Manin-Mumford, and Mordell-Lang Conjectures. Subprojects directly involving the PI: - Unlikely Intersections and o-Minimality (cooperation with J. Pila) - Reduction properties of curves in genus 2 with complex multiplication and bad reduction (cooperation with F. Pazuki) - Degenerate cases in the Zilber-Pink Conjecture / CIT (cooperation with M. Bays) - Interplay between group structure and the Bogomolov property involving small height (cooperation with R. Grizzard and L. Pottmeyer) Linda Frey is writing a Ph.D. thesis in the context of this project. Lukas Pottmeyer is a postdoc. Supported by the DFG, German Research Foundation.

Collaborations & Cooperations

2099 - Participation or Organization of Collaborations on an international level

Pazuki, Fabien, University of Copenhagen, Research cooperation

2099 - Participation or Organization of Collaborations on an international level

Pila, Jonathan, Oxford University, Research cooperation

2020 - Participation or Organization of Collaborations on an international level

Bays, Martin, University of Munster, Research cooperation

2020 - Participation or Organization of Collaborations on an international level

Grizzard, Robert, University of Wisconson, Research cooperation

Publications

Habegger, Philipp and Pila, Jonathan (2016) ‘O-minimality and certain atypical intersections’, Annales Scientifiques de l’École Normale Supérieure, 49(4), pp. 813–858. Available at: https://doi.org/10.24033/asens.2296.

URLs

Pottmeyer, Lukas (2016) ‘A Note on Extensions of ℚtr’, Journal de Théorie des Nombres de Bordeaux, 28(3), pp. 735–742. Available at: https://doi.org/10.5802/jtnb.961.

URLs

Bays, Martin and Habegger, Philipp (2015) ‘A note on divisible points of curves’, Transactions of the American Mathematical Society, 367(2), pp. 1313–1328. Available at: https://doi.org/10.1090/s0002-9947-2014-06494-5.

URLs

Grizzard, Robert, Habegger, Philipp and Pottmeyer, Lukas (2015) ‘Small points and free abelian groups’, International mathematics research notices, 20(20), pp. 10657–10679. Available at: https://doi.org/10.1093/imrn/rnv007.

URLs

Pottmeyer, Lukas (2015) ‘Heights and totally p-adic numbers’, Acta arithmetica, 171(3), pp. 277–291. Available at: https://doi.org/10.4064/aa171-3-5.

URLs

Heights and Unlikely Intersections

Research Project
|
01.04.2013
- 28.02.2017

Collaborations & Cooperations

2099 - Participation or Organization of Collaborations on an international level

Pazuki, Fabien, University of Copenhagen, Research cooperation

2099 - Participation or Organization of Collaborations on an international level

Pila, Jonathan, Oxford University, Research cooperation

2020 - Participation or Organization of Collaborations on an international level

Bays, Martin, University of Munster, Research cooperation

2020 - Participation or Organization of Collaborations on an international level

Grizzard, Robert, University of Wisconson, Research cooperation

Publications

Habegger, Philipp and Pila, Jonathan (2016) ‘O-minimality and certain atypical intersections’, Annales Scientifiques de l’École Normale Supérieure, 49(4), pp. 813–858. Available at: https://doi.org/10.24033/asens.2296.

Pottmeyer, Lukas (2016) ‘A Note on Extensions of ℚtr’, Journal de Théorie des Nombres de Bordeaux, 28(3), pp. 735–742. Available at: https://doi.org/10.5802/jtnb.961.

Bays, Martin and Habegger, Philipp (2015) ‘A note on divisible points of curves’, Transactions of the American Mathematical Society, 367(2), pp. 1313–1328. Available at: https://doi.org/10.1090/s0002-9947-2014-06494-5.

Grizzard, Robert, Habegger, Philipp and Pottmeyer, Lukas (2015) ‘Small points and free abelian groups’, International mathematics research notices, 20(20), pp. 10657–10679. Available at: https://doi.org/10.1093/imrn/rnv007.

Pottmeyer, Lukas (2015) ‘Heights and totally p-adic numbers’, Acta arithmetica, 171(3), pp. 277–291. Available at: https://doi.org/10.4064/aa171-3-5.

Members (3)

Philipp Habegger

Principal Investigator

Linda Frey

Project Member

Lukas Pottmeyer

Project Member

Research Groups

Zahlentheorie

Heights and Unlikely Intersections

Research Project | 01.04.2013 - 28.02.2017

Collaborations & Cooperations

2099 - Participation or Organization of Collaborations on an international level

Pazuki, Fabien, University of Copenhagen, Research cooperation

2099 - Participation or Organization of Collaborations on an international level

Pila, Jonathan, Oxford University, Research cooperation

2020 - Participation or Organization of Collaborations on an international level

Bays, Martin, University of Munster, Research cooperation

2020 - Participation or Organization of Collaborations on an international level

Grizzard, Robert, University of Wisconson, Research cooperation

Publications

Habegger, Philipp and Pila, Jonathan (2016) ‘O-minimality and certain atypical intersections’, Annales Scientifiques de l’École Normale Supérieure, 49(4), pp. 813–858. Available at: https://doi.org/10.24033/asens.2296.

Pottmeyer, Lukas (2016) ‘A Note on Extensions of ℚtr’, Journal de Théorie des Nombres de Bordeaux, 28(3), pp. 735–742. Available at: https://doi.org/10.5802/jtnb.961.

Bays, Martin and Habegger, Philipp (2015) ‘A note on divisible points of curves’, Transactions of the American Mathematical Society, 367(2), pp. 1313–1328. Available at: https://doi.org/10.1090/s0002-9947-2014-06494-5.

Grizzard, Robert, Habegger, Philipp and Pottmeyer, Lukas (2015) ‘Small points and free abelian groups’, International mathematics research notices, 20(20), pp. 10657–10679. Available at: https://doi.org/10.1093/imrn/rnv007.

Pottmeyer, Lukas (2015) ‘Heights and totally p-adic numbers’, Acta arithmetica, 171(3), pp. 277–291. Available at: https://doi.org/10.4064/aa171-3-5.

Members (3)

Philipp Habegger

Principal Investigator

Linda Frey

Project Member

Lukas Pottmeyer

Project Member

Research Groups

Zahlentheorie

Research Project
|
01.04.2013
- 28.02.2017