moduli of finite flat group schemes and modularity we prove that under some mild conditions a two dimensional p adic galois representation which is residually modular and potentially barsotti tate at p is modular this provides a more conceptual way of establishing the shimura taniyama weil conjecture especially for elliptic curves which acquire good reduction over a wildly ramified extension of 3 the main ingredient is a new technique for analyzing flat deformation rings it involves resolving them by spaces which parametrize finite flat group scheme models of galois representations introduction

non optimal levels of a reducible mod l modular representation let 3 be a prime and n be a square free integer prime to for each prime p dividing n let ap be either 1 or 1 we give a sufficient criterion for the existence of a newform f of weight 2 for 0 n such that the mod galois representation attached to f is reducible and upf apf for primes p dividing n the main techniques used are level raising methods based on an exact sequence due to ribet

integrality of a ratio of petersson norms and level lowering congruences we prove integrality of the ratiof f g g outside an explicit finite set of primes where g is an arithmetically normalized holomorphic newform on a shimura curve f is a normalized hecke eigenform on gl 2 with the same hecke eigenvalues as g and denotes the petersson inner product the primes dividing this ratio are shown to be closely related to certain level lowering con gruences satisfied by f and to the central values of a family of rankin selberg l functions finally we give two applications the first to proving the integral ity of a certain triple product l value and the second to the computation of the faltings height of jacobians of shimura curves

algebraic theories for name passing calculi in a theory of processes the names are atomic data items which can be exchanged and tested for identify a well known example of a calculus for name passing is the calculus where names are additionally used as communication ports we provide complete axiomatisations of late and early bisimulation equivalences in such calculi since neither of the equivalences is a congruence we also axiomatise the corresponding largest congruences we consider a few variations of the signature of the language among these a calculus of deterministic processes which is reminiscent of sequential functional programs with a conditional construct most of our axioms are shown to be independent the axiom systems differ only by a few simple axioms and reveal the similarities and the symmetries of the calculi and the equivalences

local to global compatibility on the eigencurve we generalise coleman s construction of hecke operators in families to define an action of gl2 apf on the space of overconvergent p adic modular forms extending the classical construction using this we construct a family of p adic automorphic representations of gl2 apf on the coleman mazur eigencurve we compare this with the natural family of galois representations carried by the eigencurve using the local langlands correspondence and deduce local to global compatibility away from a discrete subset extending results of carayol

variation of iwasawa invariants in hida families let gq gl2 k be an absolutely irreducible modular galois representation over a finite field k of characteristic p assume further that is p ordinary and p distinguished in the sense that the restriction of to a decomposition group at p is reducible and non scalar the hida family h of is the set of all p ordinary p stabilized newforms f with mod p galois representation isomorphic to if is unramified at p then one must also fix an unramified line in and require that the ordinary line of f reduces to this fixed line these newforms are a dense set of points in a certain p adic analytic space of overconvergent eigenforms consisting of an intersecting system of branches i e irreducible components t a indexed by the minimal primes a of a certain hecke algebra to each modular form f h one may associate the iwasawa invariants an f an f alg f and alg f the analytic resp algebraic invariants are the number of zeroes of the p adic l function resp of the characteristic power series of the dual of the selmer group of f while the invariants are the exponents of the powers of p dividing the same objects in this paper we prove the following results on the behavior of these iwasawa invariants as f varies over h

improving upon standard estimators in discrete exponential families with applications to poisson and negative binomial cases assume that xi xp are independent random observations having discrete exponential densities p1 0 ti x rj 1 i 1 p respectively a general technique of improving upon the uniform minimum variance unbiased estimator umvue of o1 op is developed under possibly weighted squared error loss functions it is shown that improved estimators can be constructed by solving a difference inequality typical difference inequalities of a fairly general type are presented and solved when specialized to poisson and negative binomial cases broad classes of estimators are given that dominate the umvue these results unify many known results in this rapidly diverging field and some of them are new especially those related to negative binomial distributions improved estimators are also obtained for the problems in which some of the observations are from poisson families and some from negative binomial families for sum of squared errors loss estimators which dominate the umvue in the discrete exponential families are also given explicitly

semi tail upper bounds on the class of admissible estimators in discrete exponential families with applications to poisson and negative binomial distributions admissibility problems involving simultaneous estimation in discrete exponential families are studied by solving difference inequalities it is shown that if an estimator is admissible under the loss function lm 6 a pi 0m 0 a 2 then in the tail i e for large values of the observations this estimator has to be less than certain bounds specific bounds called semi tail upper bounds stub are given here these stubs are not only of theoretical interest but also are sharp enough that they establish many new results two of the most interesting ones are i the establishment of brown s conjecture concerning inadmissibility of some of the estimators proposed by clevenson and zidek 1975 and ii the establishment of inadmissibility of hudson s 1978 estimator which improves upon the uniformly minimum variance unbiased estimator in negative binomial families

weights of galois representations associated to hilbert modular forms let f be a totally real field p 3 a rational prime unramified in f and p a place of f over p let gal f f gl2 fp be a two dimensional mod p galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible we specify a set of weights determined by the restriction of to inertia at p which contains all the modular weights for this proves part of a conjecture of diamond buzzard and jarvis which provides an analogue of serre s epsilon conjecture for hilbert modular forms mod p

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

testing equivalence for mobile processes the impact of applying the testing approach to a calculus of processes with dynamic communication topology is investigated a proof system is introduced that consists of two groups of laws those for strong observational equivalence and those needed to deal with invisible actions soundness and completeness of this proof system w r t a testing preorder are shown a fully abstract denotational model for the language is presented that takes advantage of reductions of processes to normal forms

special values of anticyclotomic l functions the object of this paper is to extend the results and methods of vat01 where it was shown how cases of a conjecture of mazur on the behavior of l functions in an anticyclotomic zp extension could be deduced by studying the distribution of heegner points associated to definite quaternion algebras the main result of vat01 showed that when the sign in the functional equation is 1 then the special values of the l functions in question are generically nonzero in this paper we propose to study the special values modulo a prime of q and can offer three new theorems in this direction the first result theorem 1 1 determines the iwasawa invariant of the p adic l functions of bertolini and darmon we show that is usually zero but not always when 0 we give a precise formula for the value and an interpretation of the positivity in terms of congruences the second result theorem 1 2 pertains to the case where has residue characteristic p in this case we show that the l values are typically units but again that this is not always the case for technical reasons this theorem applies only to a restricted class of but it seems rather likely that the restrictions can be lifted finally we use the result of theorem 1 2 to transfer our results from the case where the sign in the functional equation is 1 to the case of sign 1 and to derivatives of l functions this is achieved by using congruences and the sign change phenomenon exploited by bertolini darmon namely we prove a jochnowitz congruence which relates the nontriviality of a special value modulo to the nontriviality of a classical heegner point on a modular curve the result is stated in theorem 1 4 to describe these results more precisely let g denote a newform on 0 n let k denote an imaginary quadratic field of discriminant d such that d is prime to n write n n n where n is divisible only by those primes which are split in k whereas n is divisible only by primes

eaton s markov chain its conjugate partner and mathscr p admissibility suppose that x is a random variable with density f x and that x is a proper posterior corresponding to an improper prior the prior is called p admissible if the generalized bayes estimator of every bounded function of is almost admissible under squared error loss eaton showed that recurrence of the markov chain with transition density r x f x dx is a sufficient condition for p admissibility of we show that eaton s markov chain is recurrent if and only if its conjugate partner with transition density r y x f y x d is recurrent this provides a new method of establishing p admissibility often one of these two markov chains corresponds to a standard stochastic process for which there are known results on recurrence and transience for example when x is poisson and an improper gamma prior is placed on the markov chain defined by r y x is equivalent to a branching process with immigration we use this type of argument to establish p admissibility of some priors when f is a negative binomial mass function and when f is a gamma density with known shape

a theory of communicating processes with value passing a semantic theory of process algebras which allows processes to communicate values is described a behavioural theory of testing is given for such processes and is modelled by an extension of acceptance trees a proof system is also given for this model and is shown to be both sound and complete finally the model is shown to be fully abstract with respect to the behavioural theory

lattices in the cohomology of shimura curves we prove the main conjectures of breuil j reine angew math 2012 including a generalisation from the principal series to the cuspidal case and dembele j reine angew math 2012 subject to a mild global hypothesis that we make in order to apply certain r mathbb t theorems more precisely we prove a multiplicity one result for the mod p cohomology of a shimura curve at iwahori level and we show that certain apparently globally defined lattices in the cohomology of shimura curves are determined by the corresponding local p adic galois representations we also indicate a new proof of the buzzard diamond jarvis conjecture in generic cases our main tools are the geometric breuil mezard philosophy developed in emerton and gee j inst math jussieu 2012 and a new and more functorial perspective on the taylor wiles kisin patching method along the way we determine the tamely potentially barsotti tate deformation rings of generic two dimensional mod p representations generalising a result of breuil and mezard bull soc math de france 2012 in the principal series case

uniform distribution of heegner points let e be a modular elliptic curve over q of conductor n let k denote an imaginary quadratic field of discriminant d with n d 1 if p is a prime then there exists a unique zp extension k k such that gal k q acts nontrivially on gal k k the field k is called the anticyclotomic zp extension of k let e k denote the mordell weil group of e over k then a fundamental conjecture of mazur maz predicts that the size of e k is controlled by the prime factorization of n in k equivalently mazur s conjecture relates the size of the mordell weil group to the sign in the functional equation of certain l series the conjecture was verified by greenberg rohrlich and rubin in what mazur calls the exceptional case when e has complex multiplication by k more generally they settled the conjecture for certain abelian varieties with complex multiplication for a discussion of this cm case we refer the reader to gre roh and rub our goal in this paper is to treat the generic case which occurs either when e has no cm or when the field of complexmultiplications is distinct from k under certain conditions on e and k mazur s conjecture predicts that the group e k is finitely generated our main result asserts that this is in fact the case at least when p is an ordinary prime for e or when the class number of k is prime to p the main new ingredient we introduce is that of equidistribution following ideas used by ferrero andwashington to study the cyclotomic invariant more precisely we show that theheegner points associated to definite quaternion algebras are uniformly distributed on the components of a certain curve x and that the elements of a certain galois group act independently in a suitable sense this combined with a special value formula due to gross allows us to conclude that the special values of anticyclotomic l functions are almost always nonzero so that the statement about the mordell weil groups follows from the machinery of euler systems as developed by bertolini and darmon bd

lambda calculi for strict parallel functions we introduce two calculi and show that they are expressive for two canonical domains of parallel functions the first calculus is an enrichment of the lazy call by name calculus with call by value abstractions and parallel composition while in the second the usual call by name abstractions are disallowed the corresponding domains are respectively abramsky s domain d d d a lifted function space and d d d a lifted domain of strict functions these domains are lattices and we show that the parallelism is adequately represented by the join operator while call by value abstractions correspond to strict functions the proofs of the results rely on a completeness theorem for the logical presentation of the semantics

modularity of certain potentially barsotti tate galois representations where is the reduction of p these results were subject to hypotheses on the local behavior of p at x i e the restriction of p to a decomposition group at x and to irreducibility hypotheses on 1p in this paper we build on the methods of 461 451 and 121 and relax the hypotheses on local behavior in particular we treat certain adic representations which are not semistable at x but potentially semistable we do this using results of 61 generalizing a theorem of ramakrishna 321 see fontaine mazur 22 131 for a slightly different point of view the results in 61 show that certain potentially barsotti tate deformation problems are smooth allowing us to define certain universal deformations for with the necessary galoistheoretic properties to apply wiles method to carry out the proof that these deformations are indeed realized in the cohomology of modular curves i e that the universal deformation rings are hecke algebras we need to identify the corresponding cohomology groups and prove they have the modular theoretic properties needed to apply wiles method as in 151 and 121 the identification is made by matching local behavior of automorphic representations and galois representations via the local langlands correspondence together with fontaine s theory at the prime we work directly with cohomology of modular curves instead of

a semantic theory for value passing processes based on the late approach a general class of languages for value passing calculi based on the late semantic approach is defined and a concrete instantiation of the general syntax is given this is a modification of the standard ccs according to the late approach three kinds of semantics are given for this language first a plotkin style operational semantics by means of an applicative labelled transition system is introduced this is a modification of the standard labelled transition system that caters for value passing according to the late approach as an abstraction late bisimulation preorder is given then a general class of denotational models for the late semantics is defined a denotational model for the concrete language is given as an instantiation of the general class two equationally based proof systems are defined the first one which is value finitary i e only reasons about a finite number of values at each time is shown to be sound and complete with respect to this model the second proof system a value infinitary one is shown to be sound with respect to the model whereas the completeness is proven later the operational and the denotational semantics are compared and it is shown that the bisimulation preorder is finer than the preorder induced by the denotational model we also show that in general the bisimulation preorder is strictly included in the model induced preorder finally a value finitary version of the bisimulation preorder is defined and the full abstractness of the denotational model with respect to it is shown it is also shown that for ccsl the bisimulation preorder coincides with the preorder induced by the model from this we can conclude that if we allow for parameterized recursion in our language we may express processes which coincide in any algebraic domain but are distinguished by the bisimulation this shows that if we extend ccsl in this way we obtain a strictly more expressive language

a fully abstract denotational semantics for the π calculus this paper describes the construction of two set theoretic denotational models for the p calculus the models are obtained as initial solutions to domain equations in a functor category by associating with each syntactic construct of the p calculus a natural transformation over these models we obtain two interpretations for the language we also show that these models are fully abstract with respect to natural behavioural preorders over terms in the language by this we mean that two terms are related behaviourally if and only if their interpretations in the model are related the behavioural preorders are the standard versions of may and must testing adapted to the p calculus

completed cohomology of shimura curves and a p adic jacquet langlands correspondence we study indefinite quaternion algebras over totally real fields f and give an example of a cohomological construction of p adic jacquet langlands functoriality using completed cohomology we also study the tame levels of p adic automorphic forms on these quaternion algebras and give an analogue of mazur s level lowering principle

on modular forms and the inverse galois problem in this article new cases of the inverse galois problem are established the main result is that for a fixed integer n there is a positive density set of primes p such that psl2 fpn occurs as the galois group of some finite extension of the rational nu mbers these groups are obtained as projective images of residual modular galois representations moreover families of modular forms are constructed such that the images of all their resid ual galois representations are as large as a priori possible both results essentially use khare s a nd wintenberger s notion of gooddihedral primes particular care is taken in order to exclud e nontrivial inner twists 2000 mathematics subject classification 11f80 primary 12f12 11f11

notions of computation and monads abstract the calculus is considered a useful mathematical tool in the study of programming languages since programs can be identified with terms however if one goes further and uses conversion to prove equivalence of programs then a gross simplification is introduced programs are identified with total functions from values to values that may jeopardise the applicability of theoretical results in this paper we introduce calculi based on a categorical semantics for computations that provide a correct basis for proving equivalence of programs for a wide range of notions of computation

on modular representations of bar q q arising from modular forms where g is the galois group gai i q and f is a finite field of characteristic i 3 suppose that p is modular of level n i e that it arises from a weight 2 newform of level dividing n and trivial nebentypus character then p is an odd representation the matrix p c where c is a complex conjugation in g has eigenvalues 1 1 since 1 and 1 are distinct in f p is absolutely irreducible and has a model over every subfield of f containing the set trace p we assume that f has been chosen so that it is generated by this set assume that p is a prime which exactly divides n we write p i n and restrict p to a decomposition group of g for the prime p view the restriction as a representation p p of gal t p qp we say that p is finite at p 34 or 35 w if there is a finite flat f vector space scheme h over zp for which the action of gal t p qp on the f vector space h 1 p gives pp i f p 9 is finite at p if and only if pp is unramified it is clear that p is finite at p whenever p is already modular of level n p in w of 34 cf 35 serre conjectured the converse i e that if p is finite then p is modular of level n p soon thereafter mazur 1 20 proved this conjecture in the case

on ribet s level raising theorem for u 3 a well known theorem of ken ribet asserts that under certain assumptions a modular form mod o n 0 n can be lifted to yield a newform on 0 n with the same modular galois representation for further progress in the modular theory of automorphic forms one will need to understand this phenomenon for automorphic forms on reductive groups other than gl 2 in this paper we prove such a result for the unitary group of rank 3 under suitable assumptions the proof relies on the modular representation theory of p adic reductive groups 1 introduction suppose n 1 is an integer and 0 n sl 2 i s the usual hecke subgroup s2 0 n denotes the space of cusp forms of weight 2 let f s2 0 n be a new form with trivial nebentypus that is an eigen form for all the hecke operators t p with fourier expansion

admissible estimation dirichlet principles and recurrence of birth death chains on ℤ p we establish a connection between admissible simultaneous estimation and recurrence of reversible markov chains on specifically to each generalized bayes estimator of the mean of a vector of p independent poisson variables for a weighted quadratic loss we associate a variational problem and a reversible birth and death chain on the variational problem is closely related to the dirichlet principle for reversible chains studied recently by griffeath liggett and lyons under side conditions admissibility of the estimator is equivalent to zero infimal energy in the variational problem and to recurrence of the markov chain this yields analytic and probabilistic criteria for inadmissibility which are applied to establish a broad class of results and previous conjectures