153 research outputs found
Degeneration of Hodge structures over Picard modular surfaces
We study variations of Hodge structures over a Picard modular surface, and
compute the weights and types of their degenerations through the cusps of the
Baily-Borel compactification. The main tool is a theorem of Burgos and
Wildeshaus.Comment: final versio
On the optimization of conservation law models at a junction with inflow and flow distribution controls
The paper proposes a general framework to analyze control problems for
conservation law models on a network. Namely we consider a general class of
junction distribution controls and inflow controls and we establish the
compactness in of a class of flux-traces of solutions. We then derive the
existence of solutions for two optimization problems: (I) the maximization of
an integral functional depending on the flux-traces of solutions evaluated at
points of the incoming and outgoing edges; (II) the minimization of the total
variation of the optimal solutions of problem (I). Finally we provide an
equivalent variational formulation of the min-max problem (II) and we discuss
some numerical simulations for a junction with two incoming and two outgoing
edges.Comment: 29 pages, 14 figure
Algebraic classes in mixed characteristic and Andr\'e's p-adic periods
Motivated by the study of algebraic classes in mixed characteristic we define
a countable subalgebra of which we call the algebra of
Andr\'e's -adic periods. We construct a tannakian framework to study these
periods. In particular, we bound their transcendence degree and formulate the
analog of the Grothendieck period conjecture. We exhibit several examples where
special values of classical -adic functions appear as Andr\'e's -adic
periods and we relate these new conjectures to some classical problems on
algebraic classes.Comment: Comments welcome
The Hilbert symbol in the Hodge standard conjecture
We study the Hodge standard conjecture for varieties over finite fields
admitting a CM lifting, such as abelian varieties or products of K3 surfaces.
For those varieties we show that the signature predicted by the conjecture
holds true modulo . This amounts to determining the discriminant and the
Hilbert symbol of the intersection product. The first is obtained by
-adic arguments whereas the second needs a careful computation in
-adic Hodge theory.Comment: minor modifications; 29 pages, 1 figur
Semantic Subtyping for Non-Strict Languages
Semantic subtyping is an approach to define subtyping relations for type systems featuring union and intersection type connectives. It has been studied only for strict languages, and it is unsound for non-strict semantics. In this work, we study how to adapt this approach to non-strict languages: in particular, we define a type system using semantic subtyping for a functional language with a call-by-need semantics. We do so by introducing an explicit representation for divergence in the types, so that the type system distinguishes expressions that are results from those which are computations that might diverge
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