What's the state of the art of Galois Duality theory over general fields?

more specifically, is there an analogue of Poitou Tate for finite extensions of Qp(X1,...,Xs) ?

05 June 2017 1,473 3 View

In what level of generality are galois representations associated to eisenstein series for GL_n understood?

Galois representations had been associated to cusp forms over modular curves for the full modular group (the work of Deligne and the Eichler-Shimura construction) for any weight >=2,...

02 March 2017 2,946 1 View

Potentially semi stable galois representations?

Let E, K be a finite extensions of Q_p and V a finite dimensional E vector space which is also a potentially semistable G_K module (that is, V is semistable over a finite extension of K). Let K'...

05 June 2016 2,848 1 View

Theta Functions as sections of determinant bundles?

Let X be a smooth curve over k, S a noetherian scheme over k, F a vector bundle on X\times_k S, L a line bundle X\times_k S which is the pullback of a line bundle on X. The theta function...

05 June 2016 3,071 2 View

Why is the functor M_{G,X} of families of G bundles on a connected projective curve X not representable?

Let G be a reductive group over k, X a connected projective curve over k. Associate to a scheme S over a field k the set M_{G,X}(S) of isomorphism classes of G bundles on S\times X, this defines a...

04 May 2016 6,100 0 View

How do I find the primes at which an l adic representation associated to a variety is rammified?

We consider the l adic representation of a number field K constructed from an elliptic curve E over K with given rational point 0. So this is basically the natural representation R:Gal(Q^{alg}/K)...

08 September 2015 8,572 1 View

Could you recommend any books about Number Theory?

Beginner level books. High level books. Analytical Number Theory. Algebraic Number Theory. Combinatorical Number Theory. Books about partitions. Books about primes.

03 March 2021 7,174 5 View

Arena simulation - how do i model the following model in ARENA (see description) (new to ARENA)?

Hello, I'm fairly new to ARENA and I have the following problem: I have two queues in which, in each queue, a different order type arrives (both having an arrival rate of exponential 10). Order...

02 March 2021 2,431 3 View

What is Flat Lens Antenna?

28 February 2021 5,433 3 View

Can impedance of antenna be less than 50 ohms?

I am simulating helix antenna in hfss, right now, giving excitation with 50 ohms port. When I see the results of Z parameter (real). It shows lower than 50 ohms. Do not understand, if it can be...

27 February 2021 4,218 7 View

What are the application of Fixed points thoery in Chemistry.?

It is said that fixed point theory has lot of applications not in the field of mathematics only but also in various areas. So I am looking for applications in Chemistry only..

26 February 2021 3,533 1 View

How to interpolate from a time-series database ?

Hi, I am having trouble with a problem, in the field of Optimal Control and the generation of optimal time-series. Let's consider a system, whose dynamics are represented by dx/dt =...

24 February 2021 9,105 2 View

How to constrain genetic algorithm input u?

My real system (buck converter) can only take an input of 0 to 1 (duty ratio) and I need to constrain the system so the controller action keeps within this bounds. How can I do this? The code for...

22 February 2021 2,125 3 View

Helix antenna coupling problem?

Dealing with a helix antenna, made with flexible material and not rigid like using a PCB board or wire. At the beginning of the helix is too close to the ground plane, causing coupling. How can I...

21 February 2021 4,453 3 View

How to calculate the Atomic Polar Tensor using DFT ?

Dear friends, I am a beginner at DFT calculation. I have done a structure optimization using DFT- B3LYP/6-31G*, Nevertheless, I don't know How to calculate the Atomic Polar Tensor (APT) in...

17 February 2021 9,082 3 View

How can we determine the positive definiteness of multivariable polyomial? Is there any MATLAB function available for that?

Can we check the positive definiteness of a multivariable polynomial using MATLAB functions? Of course in literature, there are few complex methods that use tensor algebra. However, before going...

16 February 2021 1,218 3 View