13 citations · 25 across the 8 of their papers we have counts for
13 papers
On -fullness in number fields
Michiel Horikx, Marta Pieropan
We prove asymptotic formulas for the number of -full ideals of bounded norm in a given ideal class and for the number of -full algebraic integers of bounded Weil height.
Log geometry and lifting rational points
Leo Herr, Sara Mehidi, Marta Pieropan +1
For a morphism of schemes, we give a tropical criterion for which points of (valued in a field, discrete valuation ring, number ring, or Dedekind domain) lift to…
Points of bounded height on certain subvarieties of toric varieties
Marta Pieropan, Damaris Schindler
We combine the split torsor method and the hyperbola method for toric varieties to count rational points and Campana points of bounded height on certain subvarieties of toric varie…
On rational points on classifying stacks and Malle's conjecture
Shabnam Akhtari, Jennifer Park, Marta Pieropan +1
In this expository article, we compare Malle's conjecture on counting number fields of bounded discriminant with recent conjectures of Ellenberg--Satriano--Zureick-Brown and Darda-…
Campana points on diagonal hypersurfaces
Francesca Balestrieri, Julia Brandes, Miriam Kaesberg +3
We construct an integral model for counting Campana points of bounded height on diagonal hypersurfaces of degree greater than one, and give an asymptotic formula for their number,…
Hyperbola method on toric varieties
Marta Pieropan, Damaris Schindler
We develop a very general version of the hyperbola method which extends the known method by Blomer and Brüdern for products of projective spaces to complete smooth split toric vari…
Campana points of bounded height on vector group compactifications
Marta Pieropan, Arne Smeets, Sho Tanimoto +1
We initiate a systematic quantitative study of subsets of rational points that are integral with respect to a weighted boundary divisor on Fano orbifolds. We call the points in the…
The split torsor method for Manin's conjecture
Ulrich Derenthal, Marta Pieropan
We introduce the split torsor method to count rational points of bounded height on Fano varieties. As an application, we prove Manin's conjecture for all nonsplit quartic del Pezzo…
On rationally connected varieties over fields of characteristic
Marta Pieropan
We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic is a consequence of the existenc…
On Galois descent of complete intersections
Marta Pieropan
We introduce a notion of strict complete intersections with respect to Cox rings and we prove Galois descent for this new notion.
Imaginary quadratic points on toric varieties via universal torsors
Marta Pieropan
Inspired by a paper of Salberger we give a new proof of Manin's conjecture for toric varieties over imaginary quadratic number fields by means of universal torsor parameterizations…
Cox rings over nonclosed fields
Ulrich Derenthal, Marta Pieropan
We give a definition of Cox rings and Cox sheaves for varieties over nonclosed fields that is compatible with torsors under quasitori, including universal torsors. We study their e…
O-minimality on twisted universal torsors and Manin's conjecture over number fields
Christopher Frei, Marta Pieropan
Manin's conjecture predicts the distribution of rational points on Fano varieties. Using explicit parameterizations of rational points by integral points on universal torsors and l…