Related papers: Beautiful pairs
We construct a tower of fields from the rings $R_n$ which parametrize pairs $(X,\lambda)$, where $X$ is a deformation of a fixed one-dimensional formal group $\mathbb{X}$ of finite height $h$, together with a Drinfeld level-$n$ structure…
We study directed sets definable in o-minimal structures, showing that in expansions of ordered fields these admit cofinal definable curves, as well as a suitable analogue in expansions of ordered groups, and furthermore that no analogue…
In a series of papers [Pan0], [Pan1], [Pan2], [Pan3] we give a detailed and better structured proof of the Grothendieck--Serre's conjecture for semi-local regular rings containing a finite field. The outline of the proof is the same as in…
The homological conjectures, which date back to Peskine, Szpiro and Hochster in the late sixties, make fundamental predictions about syzygies and intersection problems in commutative algebra. They were settled long ago in the presence of a…
We prove that certain pairs of ordered structures are dependent. Among these structures are dense and tame pairs of o-minimal structures and further the real field with a multiplicative subgroup with the Mann property, regardless of whether…
We study strong types and Galois groups in model theory from a topological and descriptive-set-theoretical point of view, leaning heavily on topological dynamical tools. More precisely, we give an abstract (not model theoretic) treatment of…
In 2012, Zilber used model-theoretic techniques to show that a curve of high genus over an algebraically closed field is determined by its Jacobian (viewed only as an abstract group with a distinguished subset for an image of the curve). In…
The moduli space of stable relative maps to the projective line combines features of stable maps and admissible covers. We prove all standard Gromov-Witten classes on these moduli spaces of stable relative maps have tautological…
The assumption that an AEC is tame is a powerful assumption permitting development of stability theory for AECs with the amalgamation property. Lately several upward categoricity theorems were discovered where tameness replaces strong…
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 NTP$_2$ fields) is dense in its perfect hull. As a consequence, it is a deeply…
We show that in a stable first-order theory, the failure of higher-dimensional type amalgamation can always be witnessed by algebraic structures which we call n-ary polygroupoids. This generalizes a result of Hrushovski that failures of…
In 1927, Artin and Schreier showed that a field is real closed if and only if its absolute Galois group has order two. Inspired by this characterisation and drawing on earlier work of Neukirch, Pop conjectured the following $p$-adic…
We look at simple groups associated primarily with the general theory of Moufang buildings, and to analyze their relation to stability theory in the model theoretic sense. As it becomes quite technical in the details, a lengthy introduction…
This is the second installment of a series of papers aimed at developing a theory of Hrushovski-Kazhdan style motivic integration for certain types of nonarchimedean $o$-minimal fields, namely power-bounded $T$-convex valued fields, and…
This paper studies the combinatorics of ideals which recently appeared in ergodicity results for analytic equivalence relations. The ideals have the following topological representation. There is a separable metrizable space $X$, a…
In this short paper, we will provide a characterisation of interpretable groups in a beautiful pair (K, E) of algebraically closed fields : every interpretable group is, up to isogeny, the extension of the subgroup of E-rational points of…
We study existential theories of henselian valued fields of positive characteristic with parameters from a trivially valued subfield. Compared to previous work, we relax perfectness and separability assumptions, and instead work with the…
Kontsevich's formality theorem states that the differential graded Lie algebra of multidifferential operators on a manifold M is L-infinity-quasi-isomorphic to its cohomology. The construction of the L-infinity map is given in terms of…
We study interpretable sets in henselian and sigma-henselian valued fields with value group elementarily equivalent to Q or Z. Our first result is an Ax-Kochen-Ershov type principle for weak elimination of imaginaries in finitely ramified…
We study rank-one sheaves and stable pairs on a smooth projective complex surface. We obtain an embedding of the moduli space of limit stable pairs into a smooth space. The embedding induces a perfect obstruction theory, which, over a…