Citation
Wu, YiTao (2012) On the padic local invariant cycle theorem. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:05292012142939643
Abstract
The aim of this paper is to consider the $p$adic local invariant cycle theorem in the mixed characteristic case.
In the first part of the paper, via casebycase discussion, we construct the $p$adic specialization map, and then write out the complete conjecture in $p$adic case. We proved the theorem in good reduction and semistable reduction cases.
In the second part of the paper, by using Berthelot, Esnault and R\"{u}lling's trace morphisms in [BER], we first prove the case of coherent cohomology, then we extend it to the Witt vector cohomology, and we then get a result on the Frobeniusstable part of the Witt vector cohomology, which corresponds the slope 0 part of the rigid cohomology, we then get the general $p$adic local invariant cycle theorem.
We also give another approach in the $H^0$ and $H^1$ cases in the general case.
In the last part of the paper, based on Flach and Morin's work on the weight filtration in the $l$adic case, we consider the $p$adic analogous result (which, together with the $l$adic's result, serves as a part to prove the compatibility of the Weiletale cohomology with the Tamagawa number conjecture). This is a direct corollary of the local invariant cycle theorem by taking the weight filtration. And we also consider some typical examples that the weight filtration statement could be verified by direct computations.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  padic cohomology, specialization map, local invariant cycle theorem 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  23 May 2012 
Record Number:  CaltechTHESIS:05292012142939643 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:05292012142939643 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  7090 
Collection:  CaltechTHESIS 
Deposited By:  Yitao Wu 
Deposited On:  30 May 2012 15:47 
Last Modified:  26 Dec 2012 04:43 
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