Related papers: Hardy type derivations on fields of exponential lo…
We construct semi-orthogonal decompositions on triangulated categories of parabolic sheaves on certain kinds of logarithmic schemes. This provides a categorification of the decomposition theorems in Kummer flat K-theory due to Hagihara and…
We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: i) deforming the chiral algebra…
In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…
We recognise Harada's generalized categories of diagrams as a particular case of modules over a monad defined on a finite direct product of additive categories. We work in the dual (albeit formally equivalent) situation, that is, with…
Let X be a smooth variety over a field k, and l be a prime number invertible in k. We study the (\'etale) unramified H^3 of X with coefficients Q_l/Z_l(2) in the style of Colliot-Th\'el\`ene and Voisin. If k is separably closed, finite or…
Let $R$ be a complete discrete valuation ring with perfect residue field $k$ of positive characteristic $p$ and field of fractions $K$ of characteristic 0. In this paper we consider a $K$-1-motive $M_K$ as in [Ra] and its associated…
We study groups definable in existentially closed geometric fields with commuting derivations. Our main result is that such a group can be definably embedded in a group interpretable in the underlying geometric field. Compared to earlier…
We show that every Hardy field extends to an $\omega$-free Hardy field. This result relates to classical oscillation criteria for second-order homogeneous linear differential equations. It is essential in [10], and here we apply it to…
Exponential families encompass the distributions central to modern machine learning -- softmax, Gaussians, and Boltzmann distributions -- and underlie the theory of variational inference, entropy-regularized reinforcement learning, and…
In this paper we consider the problem of Galois descent for suitably completed algebraic K-theory of fields. One of the main results is a suitable form of rigidity for Borel-style generalized equivariant cohomology with respect to certain…
The aim is to determine the derivations of the three series of finite-dimensional Z-graded Lie superalgebras of Cartan-type over a field of characteristic p > 3, called the special odd Hamiltonian superalgebras. To that end we first…
We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the Carath\'eodory class. This resolves a problem of D.~K.~Thomas.
Given a morphism $X \to S$ of fine log schemes, we develop a geometric description of the sheaves of higher-order differentials $\Omega^n_{X/S}$ for $n > 1$, as well as a definition of the de Rham complex in terms of this description.
The notion of linear exponential comonads on symmetric monoidal categories has been used for modelling the exponential modality of linear logic. In this paper we introduce linear exponential comonads on general (possibly non-symmetric)…
We prove the finiteness of leaps of modules of $m$-integrable derivations for algebras essentially of finite type and, more generally, for schemes essentially of finite type over an algebraically closed field of positive characteristic.…
In this paper, we solve a logarithmic $\bar{\partial}$-equation on a compact K\"ahler manifold associated to a smooth divisor by using the cyclic covering trick. As applications, we discuss the closedness of logarithmic forms, injectivity…
It is proved that exponential Blaschke products are the inner functions whose derivative is in the weak Hardy space. Exponential Blaschke products are described in terms of their logarithmic means and also in terms of the behavior of the…
In this paper, we define generalized symmetric derivations on K\"{a}hler modules. We give the relationships between the projective dimensions of $\Omega^{(1)}(R/k)$ and $\Omega^{(2)}(R/k)$ by using the symmetric derivation.We then give some…
We reveal a complexity chasm, separating the trinomial and tetranomial cases, for solving univariate sparse polynomial equations over certain local fields. First, for any fixed field $K\in\{\mathbb{Q}_2,\mathbb{Q}_3,\mathbb{Q}_5,\ldots\}$,…
We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear…